solve the initial value problem. ′=−2,(0)=−4 (express numbers in exact form. use symbolic notation and fractions where needed.)

The local minimum of the of the function f(x) = {−x, x < −1} 2 − x2, x ≥ −1 is f(-1) = -1 and the local maximum of the function f(x) = {−x, x < −1} 2 − x2, x ≥ −1 is f(0) = 0.

The local minimum of the function f(x) = {−x, x < −1} 2 − x2, x ≥ −1 occurs when x = -1. This is because when x = -1, the value of the function is f(-1) = -1. This is the lowest the function can get since the function is decreasing for x < -1 and increasing for x > -1.

The local maximum of the function f(x) = {−x, x < −1} 2 − x2, x ≥ −1 occurs when x = 0. This is because when x = 0, the value of the function is f(0) = 0. This is the highest the function can get since the function is increasing for x < 0 and decreasing for x > 0.

Therefore, the local minimum of the function f(x) = {−x, x < −1} 2 − x2, x ≥ −1 is f(-1) = -1 and the local maximum of the function f(x) = {−x, x < −1} 2 − x2, x ≥ −1 is f(0) = 0.

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If  b ≠1 and  integral [tex]\int\limits^b_1[/tex](6x-9)dx where b is some real number , then value of b that make this integral equal to 0 is b = 2 .

The integral is given as  [tex]\int\limits^b_1[/tex](6x-9)dx ;

Since , at the value of (b) the given integral is 0.

So , evaluate the integral as :

⇒   [tex]\int\limits^b_1[/tex](6x-9)dx = 0  ;

⇒ [3x² - 9x]₁ᵇ = 0 ;

Simplifying further ,

we get ;

⇒ 3b² - 9b -3(1²) +9(1) = 0 ;

⇒ 3b² -9b +6 = 0 ;

⇒ b² - 3b +2 = 0 ;

On writing the above quadratic equation in factor form ,

we get ;

⇒ (b - 1)(b - 2) = 0 ;

that means b = 1   or  b = 2 , but it given that b ≠ 1 ,

So , b = 2 .

Therefore , value of b = 2 , to make the integral 0 .

The given question is incomplete , the complete question is

Let b ≠1 and consider the integral [tex]\int\limits^b_1[/tex](6x-9)dx where b is some real number.

What value of b will make this integral equal to 0 ?

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If the histogram is skewed to the right, the graph's peak will be to the left of the center.

The peak of the graph is located to the left of the center if the histogram is skewed to the right. The frequency of observations is less frequent on the right side of the graph than it is on the left.

The mean is typically higher than the median when the distribution is right-skewn. We anticipate that the mean and median will be roughly identical in value in symmetric distributions. There is a significant link between the distribution's form and how the mean and median are related.

A positively skewed distribution, sometimes referred to as a right-skewed distribution, is a type of distribution where the majority of values are concentrated around the left tail and the right tail is longer. The distribution that leans positively is the exact opposite of one that leans negatively.

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The number of those line segments which have endpoints of different colors is 40.5.

Given data :

There are 2 red, 5 green, and 3 blue points on a circle.

There are different colored endpoints on each line segment that starts at a red point and travels to either a green point or a blue point.

There are 2 red points and 7 segments from each of them, making a total of 14 segments.

There are different colored endpoints on each line segment that leaves at a green point and travels to either a red or blue point.

There are 5 green points and 8 segments from each, for a total of 40 segments.

There are different colored endpoints on each line segment that leaves at a blue point and travels to either a green point or a red point.

Each blue point has 9 segments, and there are a total of 3 blue points.

Add all the ways = 14 + 40 + 27

= 81 segments.

Number of segment = 81/2 = 40.5 Segments

Thus, the number of those line segments which have endpoints of different colors is 40.5.

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A point in the solution of the system of inequalities is (2, 0.5)

From the question, we have the following parameters that can be used in our computation:

21x>5y+49x>2y>2-28x>2y

Express properly

So, we have the following representation

21x > 5y+49

x > 2y

2 - 28x > 2y

Next, we plot the graphs of the inequality expressions on a plane

(See attachment for the graph)

The shaded region represent the solution

And a point in this region is (2, 0.5)

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According to the question

Given an isosceles triangle, ABC with AC as its base, points D and F are the midpoints of AB and BC, respectively. Let's refer to the length of BD as x.

a. In a triangle sum of all the sides is equals to 180 degrees.

So the following formula may be used to get the value of angle A:

∴ A = 180 - (2 * ZBFD)

⇒ A = 180 - (2 * 65/2)

⇒ A = 115 degrees.

b. The Pythagorean theorem,i.e.,

Perpendicular^2 + base^2 = Hypoteneuse^2

can be used to get the length of DE:

∴ (AD)^2 = x^2 + (x/2)^2

⇒ DE = AD/2

⇒ DE = √(x^2 + (x/2)^2) / 2

⇒ DE = √((13^2) + (13/2)^2) / 2

⇒ DE = √338 / 4

c. The Pythagorean theorem,i.e.,

Perpendicular^2 + base^2 = Hypoteneuse^2

can be used to determine the length of AD:

∴ (AD)^2 = x^2 + (x/2)^2

⇒ AD= √(13^2 + (13/2)^2)

⇒ AD = √338 / 2

d. We utilize the fact that the angles at a triangle's midpoints are half its angle measurements to get the measure of angle EDF.

EDF = A/2

⇒ EDF = 115/2

⇒ EDF = 57.5 degrees

The measure of each of the following are as follows :

the measure of A = 115 degree.

the measure of DE = √338/4.

the measure of AD = √338/2.

the measure of DEF =  57.5 degrees.

According to the question

Given an isosceles triangle, ABC with AC as its base, points D and F are the midpoints of AB and BC, respectively. Let's refer to the length of BD as x.

a. In a triangle sum of all the sides is equals to 180 degrees.

So the following formula may be used to get the value of angle A:

∴ A = 180 - (2 * ZBFD)

⇒ A = 180 - (2 * 65/2)

⇒ A = 115 degrees.

b. The Pythagorean theorem,i.e.,

Perpendicular^2 + base^2 = Hypoteneuse^2

can be used to get the length of DE:

∴ (AD)^2 = x^2 + (x/2)^2

⇒ DE = AD/2

⇒ DE = √(x^2 + (x/2)^2) / 2

⇒ DE = √((13^2) + (13/2)^2) / 2

⇒ DE = √338 / 4

c. The Pythagorean theorem,i.e.,

Perpendicular^2 + base^2 = Hypoteneuse^2

can be used to determine the length of AD:

∴ (AD)^2 = x^2 + (x/2)^2

⇒ AD= √(13^2 + (13/2)^2)

⇒ AD = √338 / 2

d. We utilize the fact that the angles at a triangle's midpoints are half its angle measurements to get the measure of angle EDF.

EDF = A/2

⇒ EDF = 115/2

⇒ EDF = 57.5 degrees

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The ordered pair (-2, 1) is not a solution

From the question, we have the following parameters that can be used in our computation:

6x + 5y = -7

2x - 4y = -8

The ordered pair is given as

(-2, 1)

Substitute the known values in the above equation, so, we have the following representation

6(2) + 5(-1) = -7 == false

The above equation is false

Hence, the ordered pair is not a solution

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a) The line of best fit is y = 10x  + 60

b) the grade for a student that did not study at all is 0.

What is the slope?

The slope of a line represents the change in the dependent variable (y) for a unit change in the independent variable (x). In this case, the slope of the line of best fit represents the average change in the test grade for a one hour increase in studying. To find the slope, you can use the formula:

m = (Σxy - (Σx)(Σy)/n) / (Σx² - (Σx)²/n)

a) The line of best fit is a line that best approximates the relationship between two variables. To find the line of best fit for this data, we can use the least squares method to minimize the sum of the squares of the differences between the observed data points and the line. The equation of the line of best fit is y = mx + b, where m is the slope and b is the y-intercept. The slope can be calculated as (Σxy - (Σx)(Σy)/n) / (Σx² - (Σx)²/n), and the y-intercept as (Σy - m(Σx)) / n, where n is the number of data points.

(2, 60) and (5, 90)

The slope is

y2 - y1 =  m(x2 - x1)

90 - 60 = m(5-2)

30 = 3m

m = 10

Slope line is

y - 60 = m(x - 2)

y = 10x - 20 + 80

y = 10x  + 60

b) To estimate the grade for a student that did not study at all, we can use the line of best fit and plug in x=0 for the number of hours studying. The estimated grade for a student that did not study at all would be the y-intercept of the line,

which represents the expected test grade when

x = 0

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Complete question:

B) P(t) increases as t increases toward positive infinity.

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

The population of winbug beetles after t years from 1990 is represented by the expression P(t) = 6,000 + 29,000(1 + 0.031)t.

We can see that when t grows, the exponential growth factor (1 + 0.031)t will eventually reach positive infinity. This implies that as t approaches positive infinity, the population of winbug beetles will similarly increase.

Consequently, the following is the best prediction of what will occur to the winbug beetle population in the years after 1990.

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The mean is the measure of the central tendency most likely to be affected by an outlier.

The following statement is correct.

The term "mean" is another synonym for "average." When there is an outlier in the data set, the mean suffers the most. The only measure of central tendency on which an outlier will always have an effect is the mean.

The mean is the only measure of central tendency that is affected by all values since it is calculated by dividing the total of the values by the number of observations.

The arithmetic mean is the average quantity in a given set of data. It is defined as the sum of all observations in the data divided by the total number of observations in the data. As a result, because it comprises all of the data in a series, the mean is influenced by the extreme values.

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The solution to the given inequality, 10 ≤ 2x ≤ x+9, is 5 ≤ x ≤ 9

From the question, we are to solve the given inequality

The given inequality is

10 ≤ 2x ≤ x+9

Then,

We can write that

10 ≤ 2x and 2x ≤ x+9

First, solve the inequality 10 ≤ 2x

10 ≤ 2x

Divide both sides by 2

5 ≤ x

Now, solve

2x ≤ x + 9

2x - x ≤ 9

x ≤ 9

Thus,

5 ≤ x and x ≤ 9

5 ≤ x ≤ 9

Hence, the solution is 5 ≤ x ≤ 9

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The index forms is expressed as 9. 40  × 10¹²

Index forms are simply described as representation of a number in the form of an exponential expression or a single number that is raised to a number or variable.

Other names for index forms are standard form and scientific notation.

It also explains how many times a number contains itself.

From the information given, we have that;

2 x 2.2 x 10^12 × 1.5 × 10^12/2.2 x 10^12 - 1.5 x 1012

Represented as;

2(2.2) × 10¹² × 1.5 × 10¹²/ 2.2 × 10¹² - 1. 5 × 10¹²

We can add or subtract the index forms because they have the same exponential value, we have;

4.4(1.5)× 10²⁴/0.7  × 10¹²

Find the quotient

9. 4  × 10¹²

Hence, the value is 9. 4  × 10¹²

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The perimeter and area of a parallelogram can be determined if the length and width are known.

The perimeter of a shape is simply the total length of the boundary that the shape has. It should be noted that in this case, it's gotten by adding all the length that the shape has.

Without additional information, it is not possible to determine the exact perimeter and area of each cookie. Assuming the length and width are given, we can use the formula for the perimeter of a parallelogram (2 times the sum of the length and width) and the formula for the area of a parallelogram (length times width) to find the desired quantities.

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The probability of two planes having no cracks is 0.063 and The probability of no plane having critical cracks is 0.405.

(a) The probability of one plane having a critical crack is 10% or 0.10. The probability of two planes having detectable cracks is (0.21)^2 = 0.0441. The probability of two planes having no cracks is (0.69)^2 = 0.4761. So, the desired probability is 0.10 * 0.0441 * 0.4761 = 0.063.

(b) To find the probability that at least one plane has critical cracks, we can use the complementary probability approach, i.e., finding the probability that no plane has critical cracks and then subtracting it from 1. The probability of no plane having critical cracks is (0.90)^5 = 0.595. So, the desired probability is 1 - 0.595 = 0.405.

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Answer:

To find the area of a triangle you got A=1\2×b×h

39.5cm the diameter of the circular garden whose circumference is 124.03 cm.

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications.

Perimeter refers to the total outside length of an object.

here, we have,

circumference is 124.03 cm.

i.e. pi*d= 124.03 cm.

we know,

pi = 3.14

i.e. d= 124.03/3.14

       =39.5cm

Hence, 39.5cm the diameter of the circular garden whose circumference is 124.03 cm.

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Answer:

255

Step-by-step explanation:

Let's call the number of bags of popcorn sold by Team A as "x".

The total cost for the popcorn machine rental and supplies is $15 + 0.05x.

The revenue from selling the popcorn is 0.5x.

To reach their goal of $100, they need to satisfy the equation:

$100 = 0.5x - ($15 + 0.05x)

Expanding and solving for x:

$100 = 0.5x - $15 - 0.05x

$115 = 0.45x

x = $115 / 0.45 = 255 bags of popcorn

So, Team A needs to sell 255 bags of popcorn to reach their goal of $100.

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After evaluating the given equation ∫(x²-4)dx, we get -32/3.

Integration is the process of finding the area of the region under the curve. This is done by drawing as many small rectangles covering up the area and summing up their areas. The sum approaches a limit that is equal to the region under the curve of a function. Integration is the process of finding the antiderivative of a function. If a function is integrable and if its integral over the domain is finite, with the limits specified, then it is the definite integration. If F(x) is a particular anti-derivative of f(x) on an interval I, then every anti-derivative of f(x) on I is given by ∫ f(x) dx = F(x) + C.

Here, ∫ f(x) dx represents the whole class of integral.

C is the arbitrary constant, and all the antiderivatives of f(x) on I can be obtained by assigning a particular value to C.

Here f(x) is the integrand,

The variable x in dx is called the integrator and the whole process of finding the integral is called the integration. The ∫ sign stands for the sum.

The given equation is:

∫(x²-4)dx for interval (-2,2).

Integrate the above equation, we get

∫(x²-4)dx = x³/3 -4x +c

Now, solving this for the interval (-2,2), we get

= (2³/3 - 4×2) - ((-2)³/3 - 4×-2)

= (8/3)-8 + 8/3 - 8 = -32/3

Thus, after evaluating the given equation ∫(x²-4)dx, we get -32/3.

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The number of samples for each dot plot is given as follows:

32.

The dot plot shows the number of times that each measure appears in the data-set.

Hence the dot plot in this problem shows the number of samples that had means of 10, 20, 30, 40, 50, 60, 70, 80 and 90.

Hence, the total number of samples is obtained by the number of dots in each of the dot plots, which is of 32, hence the sentence is completed as follows:

There are 32 samples in both plot A and plot B. Each dot represents one sample.

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The domain of a function is the set of possible values that can be plugged into it.

Let y = f(x) be a function where x and y are the independent and dependent variables. If a function f offers a means of successfully generating a single value y while using a value for x to that end, then that selected x-value is said to belong to the domain of f.

The range of values that can be plugged into a function is known as its domain. In a function like f, this set represents the x values. The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.

The entire range of possible values for the independent variable make up the domain of a function. In layman's terms, this definition states that the domain is the collection of all x-values that could possibly cause the function to "work" and produce actual y-values.

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The probability that the selected pool has a ph level not considered safe is approximately 0.22 (or 22%). This can be calculated using the cumulative probability of a normal distribution with a mean of 7.5 and a standard deviation of 0.2.

1. Calculate the z-score for the lower limit of 7.2: (7.2 - 7.5) / 0.2 = -1.5

2. Calculate the z-score for the upper limit of 7.8: (7.8 - 7.5) / 0.2 = 1.5

3. Calculate the cumulative probability of the lower limit: P(-1.5) = 0.0668

4. Calculate the cumulative probability of the upper limit: P(1.5) = 0.9332

5. Calculate the probability that the selected pool has a ph level not considered safe: P(not safe) = 1 - (P(1.5) - P(-1.5)) = 0.22

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Answer:

43.4 m²

Step-by-step explanation:

side 1= 4+7 m=11m

side 2=3m

height = 6.2 m

we have

the area of the trapezoid = [tex]\frac{1}{2} height*(side1+side2)[/tex]

=[tex]\frac{1}{2} *6.2*(11+3)[/tex]

=[tex]\frac{1}{2} *6.2*14[/tex]

=43.4  m²

The interquartile range of the data represented in the box-and-whisker plot is given as follows:

IQR = 3.

The measures represented in the box-and-whisker plot are given as follows:

The interquartile range is calculated as the difference between the third quartile and the first quartile.

Hence the correct value is given as follows:

IQR = 18 - 15

IQR = 3.

Meaning that the last option is the correct option.

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Answer:

Below

Step-by-step explanation:

n   = # nickels     value = 5n

(200-n) = # dimes     value = 10(200-n)

summed, these equal 1685

5n      +    10(200-n)   = 1685

5n + 2000 -10 n = 1685

-5n = -315

n = 63     then dimes = 137

By  differentiable polynomial f(x) = 0 for some x such that a < X < b , A is correct

What is an example of a differentiable function?

If a function's derivative is present at every location inside its domain, the function is said to be differentiable. If a function f(x) is differentiable at x = a, in particular, then f′(a) exists in the domain.

                        Let's examine a few instances of differentiable polynomial and transcendental functions, such as f(x) = x4 - 3x + 5.

A is correct

F receives  two equal values in different places .

consider the line between them .

it cannot be in a coustant ascent nor descent, since it must return to the minimal value .

therefore, A, either coutant or has an surprising and descending area ,

thus from Fermat's rule the derivate must be equal to zero .

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The terminal point of the vector for a length of 10 is (x, y) = (-15.8, 7).

The length of a vector can be calculated using the Pythagorean Theorem. The formula for calculating the length of a vector can be expressed as:

Length (vector) = √((x2 - x1)² + (y2 - y1)²).

In this case, the initial point is (x1, y1) = (-3, 1) and the terminal point is (x2, y2) = (x, y) = (x, 7). Substituting these values into the formula, we get:

Length = √((x - (-3))² + (7 - 1)²)

As we need the length of the vector to be 10, we can solve for x.

10 = √((x + 3)² + 6²)

100 = (x + 3)² + 36

164 = (x + 3)²

12.8 = x + 3

x = -15.8

Therefore, the terminal point of the vector for a length of 10 is (x, y) = (-15.8, 7).

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Answer: -2 (basement)

Step-by-step explanation:

20-13=7

7+10=17

17-19= -2

Answer:

the basement

20-13=7+10=17-19=-2

The answer to the question is no, there is not convincing evidence of a difference between the population proportions.

Confidence intervals are used to estimate the range of possible values of an unknown population parameter based on a sample. If the confidence interval does not contain 0, it means that the difference between the sample proportions is statistically significant, which suggests that the difference between the population proportions may also be statistically significant. However, to conclude that there is convincing evidence of a difference between the population proportions, it is important to make sure that the conditions for performing the hypothesis test have been met, such as the independence of the sample and the normality of the population.

In this case, it seems that the conditions have not been met, so we cannot use this interval to conclude that there is convincing evidence that the true proportion of men who can identify Egypt on the map is different from the true proportion of women that can identify Egypt on a map.

Therefore, the answer to the question is no, there is no convincing evidence of a difference between the population proportions.

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The answer to the question is no, there is not convincing evidence of a difference between the population proportions.

Confidence intervals are used to estimate the range of possible values of an unknown population parameter based on a sample. If the confidence interval does not contain 0, it means that the difference between the sample proportions is statistically significant, which suggests that the difference between the population proportions may also be statistically significant. However, to conclude that there is convincing evidence of a difference between the population proportions, it is important to make sure that the conditions for performing the hypothesis test have been met, such as the independence of the sample and the normality of the population.

In this case, it seems that the conditions have not been met, so we cannot use this interval to conclude that there is convincing evidence that the true proportion of men who can identify Egypt on the map is different from the true proportion of women that can identify Egypt on a map.

Therefore, the answer to the question is no, there is no convincing evidence of a difference between the population proportions.

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The value of f(-1) is 9

The value of f(x+h) is 4x + 4h + 3

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

f(x) = 4x² - 3x + 2      Now replace x with -1.

f(-1) = 4(-1)² -3(-1) + 2

f(-1) = 4 + 3 + 2

f(-1) = 9

f(x) = 4x + 3         Now replace x with x + h.

f(x+h) = 4(x+h) + 3    

Distribute and simplify

        = 4x + 4h + 3

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The fraction of resources used collectively by X individuals can be represented as X/R, where R represents the total resources available. The fraction of resources not being used is represented as (R-X)/R. The per-capita growth rate can be represented as dX/dt = kX, where k is the proportionality constant. The differential equation for the population's size is dX/dt = kX.

A detailed explanation:

a) If the current population size is X individuals, then the fraction of resources they are using collectively can be calculated as X/R, where R represents the total resources available. This calculation gives us the proportion of resources used by X individuals relative to the total resources available.

b) To calculate the fraction of resources not being used, we subtract the fraction of resources used by X individuals from 1. So, the fraction of resources not being used is (R-X)/R.

c) The per-capita rate of change of X can be represented as dX/dt = kX, where k is the proportionality constant. This equation states that the rate of change of X (dX/dt) is proportional to X and the constant of proportionality is k.

d) To convert the equation into a differential equation for the population's size, we simply make X' stand alone on the left-hand side of the equation. So, the differential equation for the population's size becomes dX/dt = kX.

e) This differential equation states that the rate of change of X (dX/dt) is proportional to X and the constant of proportionality is k. This equation can be used to model the growth of a population over time and to understand the relationship between the population size and the rate of change of the population.

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Complete questin:

If the current population size is X individuals, what fraction of the resources are they using collectively? c) In the same situation, what fraction of the resources are not being used? d) The per-capita rate of change of X can be written as 7%. The key assumption mentioned above says that this quantity is pro- portional to the expression you wrote down in part (c). Call the proportionality constant 1', and write an equation for the per-capita growth rate. e) Convert this equation into a differential equation (change equa- tion) for the population's size. (Just make X' stand alone on the left-hand side of the equation.)