1) City A and City B have increased growth in population. Write an exponential function to represent the City B’s population, y, based on the number of years that pass, x, after a period of exponential growth.
2) City A and City B have decreased growth in population. Write an exponential function to represent City B’s population, y, based on the number of years that pass, x, after a period of exponential decline.
3) Explain the similarities and differences between your GROWTH equations and your DECAY equations.
Answers
y = A * b^x
where A is the population at time x = 0, b is the growth factor, and x is the number of years that have passed. The growth factor, b, is greater than 1.
2) An exponential function to represent City B's population with decreased growth can be written as:
y = A * b^(-x)
where A is the population at time x = 0, b is the decay factor, and x is the number of years that have passed. The decay factor, b, is between 0 and 1.
3) The similarities between the growth and decay exponential functions are that in both equations, the population is a function of time (x) and the exponential function is used to model the change in population over time.
The differences between the growth and decay exponential functions are that the growth function has a growth factor (b) greater than 1, while the decay function has a decay factor (b) between 0 and 1. Additionally, in the growth function, the exponent is positive (x), meaning the population is increasing, while in the decay function, the exponent is negative (-x), meaning the population is decreasing.
Related Questions
NO LINKS!! URGENT HELP PLEASE!!!
1. What rectangle dimensions give the greatest possible area? Explain. (From the rectangle with a perimeter of 20 meters)
2. Suppose the dimensions were not restricted to whole numbers. Would this change your answer? Explain. (same as # 1)
Answers
Problem 1
L = length
W = width
P = perimeter of the rectangle
P = 2L+2W
P = 20
2L+2W = 20
L+W = 10 after dividing everything by 2.
L = 10-W
area = length*width
A = L*W
A = (10-W)*W
A = -W^2 + 10W
Let x replace W for a temporary basis.
If we graphed y = -x^2+10x, then we'd see the highest point occurs at (5, 25). This means a width of 5 meters leads to the largest area of 25 square meters.
The length would be L = 10-W = 10-5 = 5 meters as well.
It turns out that a 5 meter by 5 meter square is the best choice when trying to max out this rectangle's area.
====================================================
Problem 2
The results we got from the previous section was that a 5 by 5 square will max out the area.
If we allowed non-whole numbers into the mix, then it wouldn't change the previous answer. The best choice is still that 5 by 5 square.
The answer only would change if the result of the previous section was some non-integer value.
The radius of a circle is 4.5 cm.find the circumference to the nearest tenth
Answers
Answer:
28.26cm
Step-by-step explanation:
The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle.
Plugging in r = 4.5 cm, we get:
C = 2π * 4.5 = 9π cm
To find the value of C to the nearest tenth, we can approximate π to 3.14:
C = 9 * 3.14 = 28.26 cm
Solve for the value of w.
(4w-8)°
(3w+6)°
Answers
Answer: To find the value of w, we need to set the expressions equal to each other:
(4w-8) = (3w+6)
Subtracting 3w from both sides:
w - 8 = 6
Adding 8 to both sides:
w = 14
So the value of w is 14.
Step-by-step explanation:
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Answers
The great pyramids of Giza are a set of ancient Egyptian structures large enough to be visible from space. Can you prove the front faces of the two pyramids are congruent triangles? Why or why not?
Answers
It cannot be proven that the front faces are congruent triangles.
Can you prove the front faces of the two pyramids are congruent triangles?No, I cannot prove that the front faces of the two pyramids of Giza are congruent triangles. The exact dimensions and shapes of the pyramids have been lost to history, and the information we have today is based on estimates and interpretations of archaeological evidence.
The exact shape of the pyramids is still the subject of some debate among experts, and there is no consensus on whether the front faces are congruent triangles.
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Elisa needs money to repair her home air conditioner, so she pawns her bicycle. The pawnbroker loans Elisa $270. Twenty four days later, Elisa gets her bicycle back by paying the pawnbroker $313.20. What annual simple interest rate did the pawnbroker charge Elisa? Assume 360 days in a year. Round simple interest rate to the nearest whole number as needed.
Answers
Elisa was charged a basic interest rate of 120% per year by the pawnbroker since she needed the money to fix her house air conditioner.
what is interest ?By dividing the initial by the interest income, the aging process, and other factors, simple interest is determined. Simple yield equals principal plus interest full days is the concept used in marketing. The easiest thing to compute interest is to employ this method. The most frequent method for calculating it is as a portion of the outstanding sum. For example, if he takes $100 from a buddy and undertakes to return the loan at 5% interest, he will only spend his share of the 100% interest. $100 (0.05) = $5. When you borrow money, you must make payments, and you must pay the interest whenever you lend it. Typically, interest is computed as an indicator of the overall of the loan total. The loan's interest is the name given to this percentage.
given
I = PRT/100
Simple interest (I) is calculated as follows: amount - principal ($279.90 - $270) = $9.90
P (principal) is the $270 loan made to Elisa.
R is the interest rate on a yearly basis.
The loan's amortisation period, or T (time), is 11 days, or 11/360 years.
9.9 = 270 × R × 11/360 × 1/100
R = (9.9×360×100)/(270×11) = 120%
120% is the annual simple interest rate.
Elisa was charged a basic interest rate of 120% per year by the pawnbroker since she needed the money to fix her house air conditioner.
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we consider a triangle CDE such that : CD = 3,6cm ; CE = 4,2cm and DE = 5,5
Is the triangle CDE rectangular?
Answers
The given triangle CDE is not Rectangular.
What are types of triangles ?
Acute triangle . . . all three angles are less than 90°
Right triangle . . . one angle is 90°
Obtuse triangle . . . one angle is greater than 90°
Equilateral triangle . . . all three sides are the same length
Isosceles triangle . . . two sides are the same length
Scalene triangle . . . all three sides are different lengths
Given:
CD = 36cm ; CE = 42cm and DE = 55
Hence , the given triangle CDE is not Rectangular.
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y = 2x + 3
y = 8/4 x - 1/4
how many solutions
Answers
Answer: The number of solutions for the system of linear equations depends on whether the lines are parallel or intersect at a single point. If the lines are parallel, there are no solutions, as they never meet. If the lines intersect at a single point, there is exactly one solution.
To determine the number of solutions, we need to find the point of intersection of the two lines. We can do this by solving for x in one equation and substituting it into the other equation:
2x + 3 = 8/4 x - 1/4
8x + 12 = 2x - 1/2
6x = - 12.5
x = -2.08
Then, substituting this value of x back into either equation to find the corresponding value of y:
y = 2 * (-2.08) + 3 = 0.16
So, the two lines intersect at the point (-2.08, 0.16), which means there is exactly one solution to the system of linear equations.
Step-by-step explanation:
The length of a rectangle is 8 feet longer than the width. If the perimeter is 88 feet, find the length and width of the rectangle.
Answers
Check the picture below.
[tex]\textit{perimeter of a rectangle}\\\\ P=2(L+w) ~~ \begin{cases} L=length\\ w=width\\[-0.5em] \hrulefill\\ P=88\\ L=w+8 \end{cases}\implies 88=2( ~~(w+8)+w ~~ ) \\\\\\ 88=2(2w+8)\implies 88=4(w+4)\implies \cfrac{88}{4}=w+4 \\\\\\ 44=w+4\implies \boxed{40=w}\hspace{5em}\stackrel{w+8}{\boxed{L=48}}[/tex]
A test to determine whether a certain antibody is present is 99.5% effective. This means that the test will accurately come back negative if the antibody is not present (in the testsubject) 99.5% of the time. The probability of a test coming back positive when the antibody is not present (a false positive) is 0.005. Suppose the test is given to five randomly selected people who do not have the antibody.
(a) What is the probability that the test comes back negative for all five people?
(b) What is the probability that the test comes back positive for at least one of the five people?
Answers
The probability that the test is negative for all people is: P = 0.9655 and probability that the test comes back positive for at least one of the five people is P = 0.0344.
What is probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.
The probability that the test is negative for all people is:
[tex]P = (0.995)^7[/tex]
P = 0.9655
b. The probability that the test comes back positive for at least one of the five people:
P = 1 - P (Negative for all 5)
P = 1 - 0.9655
P = 0.0344
Hence, the probability that the test is negative for all people is: P = 0.9655 and probability that the test comes back positive for at least one of the five people is P = 0.0344.
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determine the solutions of the equation: the absolute value quantity four thirds times x plus 2 end quantity minus 6 equals 0
Answers
the solutions of the equation are x = -1.5 and x = 2.
The solutions of the equation are x = -1.5 and x = 2.
Absolute value equation: |4/3x + 2| - 6 = 0
Equation inside absolute value must equal 0:
4/3x + 2 - 6 = 0
4/3x = -4
x = -4 * (3/4)
x = -1.5
Equation inside absolute value must equal 0:
4/3x + 2 + 6 = 0
4/3x = -8
x = -8 * (3/4)
x = 2
The absolute value quantity of four thirds times x plus 2 end quantity minus six equals zero can be written as:
|4/3x + 2| - 6 = 0
This equation can be rewritten as two separate equations as follows:
4/3x + 2 - 6 = 0
4/3x + 2 + 6 = 0
Solving the first equation:
4/3x + 2 - 6 = 0
4/3x = -4
x = -4 * (3/4)
x = -1.5
Solving the second equation:
4/3x + 2 + 6 = 0
4/3x = -8
x = -8 * (3/4)
x = 2
Therefore, the solutions of the equation are x = -1.5 and x = 2.
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David sold his house for $159,00 He got this amount knowing that he would have to pay a 6% commission to his agent. What amount did he have after the agent was paid?
Answers
Use the logical equivalences p → q ≡ ~p∨ q and p ↔ q ≡ (~p∨ q) ∧ (~ q∨ p) to rewrite the given statement forms without using the symbol → or ↔.
a) (p → r) ↔ (q → r)
Answers
The logical equivalence for the given statement is (p → r) ↔ (q → r)≡ (~p∨r)∧(~q∨r).
What is the logical equivalence?Logical equivalence is the condition of equality that exists between two statements or sentences in propositional logic or Boolean algebra.
Given that, p → q ≡ ~p∨q and p ↔ q ≡ (~p∨q)∧(~q∨ p)
a) (p → r) ↔ (q → r)
Now, (p → r)≡ ~p∨r
(q → r)= ~q∨r
So, (p → r) ↔ (q → r)≡ (~p∨r)∧(~q∨r)
Therefore, the logical equivalence for the given statement is (p → r) ↔ (q → r)≡ (~p∨r)∧(~q∨r).
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Given the equation 6.78w = 16.611, solve for w.
2.45
9.831
23.391
112.62
Answers
Step by Step Explanation:
When you have a variable next to a number, this means we are multiplying.
To solve for w, you need to figure out what number can you multiply 6.78 with to get 16.611.
Let's try solving this out step by step!
1. Let's say 2.45 was w. We will solve to see if it will give us 16.611.
6.78 × 2.45 = 16.611, so this means that 2.45 is the correct answer.
2. Let's say 9.831 was w. We will solve to see if it will give us 16.611.
6.78 × 9.831 = 66.65418, so this means that 9.821 is not the correct answer.
3. Let's say 23.391 was w. We will solve to see if it will give us 16.611.
6.78 × 23.391 = 158.59098, so this means that 23.391 is not the correct answer.
4. Let's say 112.62 was w. We will solve to see if it will give us 16.611.
6.78 × 112.62 = 763.5636, so this means that 112.62 is not the correct answer.
This leaves us off to know that 2.45 = w, so 2.45 is the correct answer.
In AABC, the angle bisector of ZB also bisects AC. Classify AABC as
specifically
as possible.
Answers
Answer:
∆ABC is an isosceles triangle
Step-by-step explanation:
You have a triangle ABC such that the angle bisector of angle B also bisects side AC.
Angle bisectorAn angle bisector divides the sides of the triangle proportionally. This means the sides BA and BC will have the same ratio as the segments of AC on either side of the point of intersection with the angle bisector.
Since AC is bisected, that means those segments are congruent, hence sides BA and BC are congruent. The triangle is isosceles.
Kelsey’s neighborhood has a straight road with stop signs at both ends and a fire hydrant at its midpoint. On a map, the fire hydrant is located at (12,7) and one of the stop signs is located at (3,11). Where on the map is the other stop sign located?
Answers
Answer: (21, 3)
Step-by-step explanation:
Select the correct answer.
Which inequality is equivalent to the given inequality?
-4(x + 7) < 3(z - 2)
OA. -7z<-34
OB. -7z > -34
OC. -7> 22
OD. -7z < 22
Answers
-22 < 7x is the inequality that is equivalent to the given inequality.
What is inequality?
An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including:
The symbol a < b indicates that an is smaller than b.
When a > b is used, it indicates that an is bigger than b.
Here, we have
Given: -4(x + 7) < 3(x - 2)
To find out which inequality is equivalent, you solve for x.
-4(x+7) < 3(x-2): distribute variables
-4x-28 < 3x-6: Add 6 to both sided
-4x-22 < 3x: add 4x to both sides
-22 < 7x
Hence, -22 < 7x is the inequality that is equivalent to the given inequality.
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Terrance buys 6 bottles of sports drink. He has coupons for $0.55 off the regular price of each bottle. After using the coupons, the total cost of the sports drinks is $4.44. Which equation can be used to find the regular price p of a bottle of sports drink?
Answers
Answer:
(4.44 + 0.55n) / n = p
(4.44 + 0.55 * 6) / 6 = p
(4.44 + 3.3) / 6 = p
(7.74) / 6 = p
1.29 = p
or
4.44 / 6 + 0.55 = p
Step-by-step explanation:
n = number of bottles
p = 1.29
According to a recent survey, the probability that the driver in a fatal vehicle accident is female (event F) is 0.2058. The probability that the driver is 24 years old or less (event A) is 0.1887. The probability that the driver is female and is 24 years old or less is 0.0582. Answer parts (a) through (d) below.
Question content area bottom
(b) Find the probability of F′∪A.
Answers
The probability of F′∪A 0.9829
How to solve for the probability
The probability can be defined as the likelihood that an event is going to happen.
We are to find the probability F′∪A.
What is F'
This is gotten as 1 - probability of F
F' = 1 - 0.2058
F' = 0.7942
Then we are to get the probability of event A from the question
P(A) = 0.1887
Hence the probability of F′∪A.
= P(A) + P(F`)
= 0.1887 + 0.7942
= 0.9829
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At a school play, there is a spotlight above the center of
the floor that covers a lighted area with a radius of 7 feet.
What is the area covered by the spotlight?
Area = 3.14*r²
Answers
According to the question we have ,The area covered by the spotlight is 153.86 square feet. The correct option is c.
What are diameter and radius?The diameter of a circle cuts through center whereas the radius extends from the center to the edges of the circle. A circle's diameter effectively splits the shape in half. The radius of a circle is the distance from the middle to any point on the edge. The diameter the radius are inversely proportional, or 2r=d2 r=d. A line connecting two points on either a circle is referred to as a chord.
We have the formula of Area of a circle: A = π[tex]r^2.[/tex]
According to the question we have ,there is a spotlight above the center of the ground that surrounds a 7-foot-radius lit area.
A = π[tex]r^2[/tex]. = π * [tex]7^2[/tex]
= 3.14 * 49 = 153.86 square feet.
So, the area covered by the spotlight is 153.86 square feet.
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please help immediately what is the input if the output is 7
Answers
The side length of a square with area of 7 units squared is given as follows:
2.65 units.
How to obtain the area of a square?The area of a square of side length s is given by the side length squared, according to the equation given as follows:
A = s².
In this problem, we have that the output is of 7, that is, the area of the square is of seven, hence the side length of the square is given as follows:
s² = 7
s = sqrt(7)
s = 2.65 units.
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Solve the following compound inequality for x
and express your answer in interval notation.
Assume x is an element of the real number system.
11 < 3x-2 ≤ 19
Answers
x is a component of the real number system 11 < 3x-2 ≤ 19, although as a compound inequality, it also belongs to 13/3 and 7.
what is inequality ?A interaction between two terms or concepts that is neither equal in mathematics is referred to as an inequality. Consequently, inequity results from imbalance. In algebra, an inequality establishes the connection between two non-equal numbers. Egality and inequalities are not the same. Use the not comparable symbol most usually when two components are really not equal (). Values of any size can be contrasted using a variety of inequalities. By changing the two aspects until only the variables are left, many straightforward inequalities can be solved. But, a variety of factors support inequality: Both sides' 0 are split or added. Exchange the left and the right.
given
11 < 3x-2 ≤ 19
11< 3x-2
3x-2 ≤ 19
11+ 2 < (3x-2)+ 2
(3x-2)+ 2 ≤ 19 + 2
x belongs to 13/3 and 7
x is a component of the real number system 11 < 3x-2 ≤ 19, although as a compound inequality, it also belongs to 13/3 and 7.
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The movement of the progress bar may be uneven because questions.co be worth more or less (inc
Choose the fraction pair that is equivalent.
O and
4 and 20
and
and/
Answers
The fraction pairs that are equivalent to 4 and 20 is given as follows:
2 and 10 = 2/10.1 and 5 = 1/5.What are equivalent fractions?Equivalent fractions are fractions that have the same denominator.
The fraction for this problem is given as follows:
4/20.
Dividing both the numerator and the denominator by 2, an equivalent fraction is given as follows:
2/10.
Dividing again by two, we have that:
1/5.
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15 bakers comple an order in 24 hrs how much time would it take for 18 bakers to complete same order
Answers
Answer:
15×24
times 15and24
giving you this answer
120
then divide 120 by 18
=20hrs would take the Baker
Answer:
28.8 hours
Step-by-step explanation:
[tex]\frac{24 .hours}{15 .bakers}[/tex] = 1.6 hours per baker
1.6 x 18 = 28.8 hours for 18 bakers to complete that order
3. Mr. Jackson could think about his experiment a little differently. How many times should he expect to roll a 4 if he rolls his number cube 30 times? This is called the mean, or expected value. You can find it if you know the number of trials and the probability of success for an individual trial. Use the formula μx = np to find the expected value.
Answers
The sample size based on the information is 30.
The probability is 0.1667.
How to calculate the valueFrom the information, Mr. Jackson could think about his experiment a little differently. How many times should he expect to roll a 4 if he rolls his number cube 30 times? This is called the mean, or expected value.
The Sample size , n = 30. The Probability of an event of interest, p = 0.1667
The Mean will be:
= np = 30 * 0.167
= 5.000
Standard deviation will be:
= √(np(1-p)) = √ 4.1667
= 2.04
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If $300 is invested for 3 years with an interest rate of 6%
per annum, calculate the final balance, rounded to the
nearest cent, if:
Simple interest was used
Answers
The required final balance on interest rate of 6%per annul is $354.
What is interest?The fee you pay to borrow money or the fee you charge to lend money is called interest. The most common way to represent interest is as a yearly percentage of the loan amount. The interest rate on the loan is known as this percentage.
According to question:Simple interest is calculated as:
I = P * r * t
where I is the interest, P is the principal (initial investment), r is the annual interest rate as a decimal, and t is the number of years.
So, in this case:
I = 300 * 0.06 * 3
I = 300 * 0.06 * 3 = 54
The final balance would be the sum of the initial investment and the interest earned:
Final balance = P + I
Final balance = 300 + 54
Final balance = 300 + 54 = 354
Rounded to the nearest cent, the final balance is $354.
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Estimate : 0.93 x 2.6
After that:
Estimate: 93 x 0.26
After That :
Estimate: 9.3 x 26
After That
Estimate: 0.93 x 0.26
Answers
The value of the equations are
A = 0.93 x 2.6 = 2.418
B = 93 x 0.26 = 24.18
C = 9.3 x 26 = 241.8
D = 0.93 x 0.26 = 0.2418
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
a)
A = 0.93 x 2.6 be equation (1)
On simplifying the equation , we get
A = 2.418
b)
B = 93 x 0.26 be equation (2)
On simplifying the equation , we get
B = 24.18
c)
C = 9.3 x 26 be equation (3)
On simplifying the equation , we get
C = 241.8
d)
D = 0.93 x 0.26 be equation (4)
On simplifying the equation , we get
D = 0.2418
Hence , the equations are solved
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Write an equation for the nth term of each arithmetic sequence. Then find the 12th term of the sequence.
as = -9, d = 2
Answers
Answer:
Step-by-step explanation:The equation for the nth term of an arithmetic sequence is given by:
an = a1 + (n-1)d
Where:
a1 is the first term of the sequence
d is the common difference
n is the number of the term we want to find
Using the given information, we have:
a1 = -9 and d = 2
Plugging these values into the formula, we get:
an = -9 + (n-1)2
To find the 12th term of the sequence:
n = 12
an = -9 + (12-1)2
an = -9 + 11 * 2
an = -9 + 22
an = 13
So the 12th term of the sequence is 13.
when you have an exponent outside of parenthesis, do you do the parenthesis first?
Answers
Answer: Yes.
Step-by-step explanation: Follow PEMDAS.
P: PARENTHESIS
E: EXPONENTS
M: MULTIPLY
D: DIVIDE
A: ADDITION
S: SUBTRACT
Someone to help me hereeeee
Answers
Answer: 485 is the answer.
Step-by-step explanation: