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Related Questions
The population of a pigeons in a city is 100 and is growing exponentially at 20% per year. Write a function to represent the population of pigeons after
t
t years, where the monthly rate of change can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage rate of change per month, to the nearest hundredth of a percent
Answers
Answer:
p(t) = 100×1.0153^(12t)1.53% per monthStep-by-step explanation:
In general, the function will be written ...
p(t) = (initial value)×(growth factor)^t
where t is in units comparable to those applicable to the growth factor. The growth factor is found from ...
growth factor = 1 + growth rate
Here, the growth rate is given as 20% per year, so the growth factor per year is ...
1 +20% = 1.20
The initial value is given as 100, so we can write the exponential function as ...
p(t) = 100×1.20^t
__
The time period units for t are supposed to be years, but we want to find the growth rate for a month. We can do that by recognizing there are 12 months in a year. In the above equation, we can use (1/12)(12t) in place of t, then figure the growth factor (and growth rate) per month.
p(t) = 100×(1.20^(1/12))^( 12t)
p(t) = 100×1.0153^(12t) . . . . population exponential function
This shows the monthly growth factor is 1.0153, so the monthly rate of change (growth rate) is ...
1.0153 -1 = 0.0153 = 1.53% . . . . monthly rate of change
Answers:
Function is [tex]P(t) = 100(1.0153)^{12t}\\\\[/tex]Monthly growth rate is roughly 1.53%=====================================================
Explanation:
The population starts at 100 pigeons. After a year, the population goes up by 20%, meaning the population goes up by 20. It lands on 120 after a full year (100+20 = 120).
Dividing the "before" and "after" population amounts gets us 120/100 = 1.20
If we didn't worry about the monthly rate, and only cared about the annual rate of growth, then the population function would be
[tex]P(t) = 100(1.20)^t[/tex]
where t is the number of years and P(t) is the population for that year number. Notice how the 1.20 is the base of the exponential to quickly tell the reader the annual rate of growth. We read off the .20 portion and that converts to 20% after moving the decimal 2 spots to the right.
If we were to plug t = 0 into that function, then we'd get P(0) = 100. Inputting t = 1 leads to P(1) = 120. This helps confirm we have the correct annual growth rate function.
---------------------
Unfortunately, your teacher doesn't want the annual growth rate function. Instead, they want you to write a function where the reader can easily pick out the monthly rate of change without having to do any math. This is due to the instructions that "the monthly rate of change can be found from a constant in the function". Let m be this constant.
Since t is the number of years, this means t = 1/12 represents 1/12 of a year, aka 1 month. If you were to compute P(1/12), then you should get roughly 101.530947049973
Divide this amount over the initial population to find m.
m = 101.530947049973/100 = 1.01530947049973
So we get m = 1.0153 after rounding to four decimal places.
The number m is in the form 1+x. Solving 1+x = m will lead to x = 0.0153 to indicate a monthly rate of change is roughly 1.53% since we move the decimal point 2 spots to the right to go from 0.0153 to 1.53%
The pigeon population is increasing by roughly 1.53% each month.
This is why computing this m value leads to the reader able to spot the monthly rate of change without having to resort to a calculator. All they have to do is read the digits to the right of the decimal point and convert that to percentage form.
---------------------
An alternative way to compute this value is to use this formula
m = (1+r)^(1/12)
We'll plug in the annual rate r = 0.20 to get:
m = (1+r)^(1/12)
m = (1+0.20)^(1/12)
m = 1.01530947049973
m = 1.0153
We get the same approximate value as earlier.
---------------------
Whichever method you use, you should get roughly m = 1.0153
We're given that A = 100 is the initial population
So we'll then be able to form this function
[tex]P(t) = A*(m)^{12t}\\\\P(t) = 100(1.0153)^{12t}\\\\[/tex]
This represents the monthly growth of the population where t is in years. Note that after something like t = 3 years, we have 12t = 12*3 = 36 months pass by. So that's why the 12t is in the exponent rather than simply t.
Once again, for comparison we have...
[tex]P(t) = 100(1.20)^{t}\\\\[/tex] for annual growth[tex]P(t) = 100(1.0153)^{12t}\\\\[/tex] for monthly growthEach function has t represent the number of years. The difference is the base of each exponential to tell us the respective annual or monthly growth rate. Also, the exponent up top must be adjusted depending on which you go for.
---------------------
You may be wondering: "what if the exponent in the monthly growth rate function wasn't 12t?". Let's find out. We'll assume the monthly growth rate function is [tex]P(t) = 100(1.0153)^{t}\\\\[/tex] and show that an error happens.
If we plugged in something like t = 1, we should get P(t) = 120 like mentioned earlier.
[tex]P(t) = 100(1.0153)^{t}\\\\P(1) = 100(1.0153)^{1}\\\\P(1) = 100(1.0153)\\\\P(1) = 101.53\\\\[/tex]
That value of 101.53 is the approximate population number after 1 month, rather than 1 year. Making the exponent 12t will fix the issue.
find the domain of y=1/2 square root of x+2-3
Answers
Does (2, –2) make the equation y = –2x + –2 true?
Answers
Answer: no it doesn’t because -2 doesn’t equal to -6
Step-by-step explanation:
all you have to do is plug 2 for x value and -2 for y
-2= -2(2)+ -2
so -2= -4+ -2 and -4+ -2 is -6
therefor -2 doesn’t equal to -6
Which problem will have the greater quotient, 376.0 divided by 93 OR 376 divided by 93.01?
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Answer: The first option.
Explanation: 376/93 = 4 4/94, while 376/93.01 = 4.04257606709....., which is less than 4 4/94, therefore the first option has the greatest quotient.
Please solve this...I can;t do it do it
Answers
Answer:
Area = 867 meters
Step-by-step explanation:
You have a rectangle. This means opposite sides are equal. If you set these expressions equal to each other, you will get two equations with two unknowns, x and y. Next, solve the system of equations to find x and y. Then, use the values to find the length and width of the rectangle. Last, multiply length × width to find the area.
The graph below shows the water level in a tank being drained at a
constant rate. What does the Y-intercept of the graph represent? *
Tank Water Level
16
14
12
10
(1, 10)
Height (in.)
(4,4)
01234567
Time (h)
O The initial height of the water before any water drained out.
The number of hours it takes to completely empty the tank of water
O The number of hours needed to drain 1 inch of water from the tank
The number of inches that the tank can hold
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Answer:
the initial height of water.
Step-by-step explanation:
when time equals zero, no water has been drained.
the volume of the tank is unknown however the volume in the tank is 12 at time zero
Porfa ayúdenme a resolver lo de la ficha, plis.
Answers
Answer:
Step-by-step explanation:
Portf?
How do I solve this problem?
Answers
How can I Graph
-7x= -105
Answers
Answer:
see explanation
Step-by-step explanation:
- 7x = - 105 ( divide both sides by - 7 )
x = 15
A line with equation x = c is a vertical line parallel to the y- axis passing through all points with an x- coordinate of c
Thus x = 15 is a vertical line passing through all points with an x- coordinate of 15
Plot (15, 0 ) , (15, 3 ) and (15, - 3) and join a straight line through them for graph
Let f(x)=root2x. If the rate of change of f at x=c is four times its rate of change at x=1 then c=?
Answers
Answer:
[tex]c=\frac{1}{16}[/tex]
Step-by-step explanation:
[tex]f(x)=\sqrt{2x}[/tex]
[tex]f'(x)=\frac{\sqrt{2x}}{2x}[/tex]
[tex]f'(1)=\frac{\sqrt{2}}{2}[/tex]
[tex]f'(c)=\frac{\sqrt{2c}}{2c}[/tex]
[tex]f'(c)=4f'(1)[/tex]
[tex]\frac{\sqrt{2c}}{2c}=4(\frac{\sqrt{2}}{2})[/tex]
[tex]\frac{\sqrt{2c}}{2c}=2\sqrt{2}[/tex]
[tex]\sqrt{2c}=4c\sqrt{2}[/tex]
[tex]2c=32c^2[/tex]
[tex]2=32c[/tex]
[tex]\frac{1}{16}=c[/tex]
Is this graph a function or not a function
Answers
Answer:
No, it doesn't pass the vertical line test.
Step-by-step explanation:
Which set of numbers are ordered from least to greatest?
O A. 7,1-41, -7,0,-131, 3
B. -31, -7,0,3,7, 1-4]
C. -7,-131,0,3, 4,7
D. 7.1-41,3,0.-131, -7
Answers
Which condition in the figure below will prove l || m?
Answers
Answer:
m<2 + m<3 = 180°
Step-by-step explanation:
Lines intersected by a transversal are parallel if same-side interior angles are supplementary.
Answer: m<2 + m<3 = 180°
Someone please help me
Answers
This graph represents the design of a child’s slide what is the slope of the slide
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Answer:
I think it is 1/2 because it goes up 1 over 2
As a car owner/lessee, it is not a requirement to have minimum coverage auto insurance.
T or F
Answers
Answer: False
Step-by-step explanation:
Calculate the distance between the points M=(-1,-2) and C=(-9, 2) in the coordinate plane.
Round your answer to the nearest hundredth.
Answers
Answer:
8.9443
Step-by-step explanation:
d = √((x2-x1)2 + (y2-y1)2)
Step by step procedure:
Find the difference between coordinates:
(x2-x1) = (-9 - -1) = -8
(y2-y1) = (2 - -2) = 4
Square the results and sum them up:
(-8)2 + (4)2 = 64 + 16 = 80
Now Find the square root and that's your result:
Exact solution: √80 = 4√5
Approximate solution: 8.9443
Please help meeeeeeeeeeeeeeeeeeeeeeeeeeeee ty :)
Answers
We know the equation.
=> y = mx + bWe also know the y-intercept is -1.
=> y = mx - 1All we need to do now is to find the slope. We know the slope formula.
=> Rise/Run = Slope=> 4/6 = Slope=> 2/3 = SlopeConclusion:Therefore, our equation is y = 2x/3 - 1
Hoped this helped.
[tex]BrainiacUser1357[/tex]
What is the answer please give i really help and no links
Answers
Answer:
[tex]9\frac{57}{63}[/tex]
Step-by-step explanation:
First, we need to turn them into improper fractions:
[tex]2\frac{4}{7}[/tex] + [tex]7\frac{3}{9}[/tex]
7 x 2 + 4
7 x 9 + 3
[tex]\frac{18}{7}[/tex] + [tex]\frac{66}{9}[/tex]
Next, we need to find a common multiple of both 7 and 9
7, 14, 21, 28, 35, 42, 49, 56, 63
9, 18, 27, 36, 45, 54, 63
So the denomonator turns into 63.
We've multiplied the denomonater 9 times for the first fraction and 7 times for the second fraction, we therefore have to do the same to the numerator.
18 x 9 = 162
66 x 7 = 462
[tex]\frac{162}{63}[/tex] + [tex]\frac{462}{63}[/tex] = [tex]\frac{624}{63}[/tex]
Next, we have to turn it back into a mixed number.
To work it out: 624 / 63 = 9 (1 s.f) <--- Mixed number.
9 x 63 = 567
624 - 567 = 57 (Working out the remainder.)
Combining them, the answer is therefore [tex]9\frac{57}{63}[/tex]
Hope this helps and have a good day!
10. Sarah wants to buy shirts for her school's
graduation party. A company will make the
shirts for $10.50 each plus a $50 setup
charge. If Sarah has $1000, which inequality
could she use to find the maximum number
of x shirts she can buy?
Answers
Answer:
1000 ≥ 10.50x + 50
Step-by-step explanation:
≥ is a greater than or equal to sign. We want to know how many she could possibly buy.
.this is all the question
Answers
Answer:
Answer: 2
Step-by-step explanation:
The value of y varies directly with x.
When y=3, x=1.
What is the value of y when x is 4?
12
3/4
4 1/3
8
Answers
Answer:
12
Step-by-step explanation:
x = 1 y = 3, x = 2 y = 6, x = 3 y = 9, x = 4 y = 12
Answer:
12
Step-by-step explanation:
if x=1 , y =3
if x=4 then y=3×4=12
y=12
Can someone help answer b plzzz
Answers
80 x.70 is 56 as you wrote, and it says 70% wait LESS THAN 30 minutes
On the left of the graph, time, you go to 30 minutes and the patients are much less (21) than 56 patients
ANSWER: No
An exponential growth function has an asymptote of y = –3. Which might have occurred in the original function to permit the range to include negative numbers?
A whole number constant could have been added to the exponential expression.
A whole number constant could have been subtracted from the exponential expression.
A whole number constant could have been added to the exponent.
A whole number constant could have been subtracted from the exponent.
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The right choice is: A whole number constant could have been subtracted from the exponential expression.
Let be an exponential function of the form [tex]y = A\cdot e^{B\cdot x}[/tex], where [tex]A[/tex] and [tex]B[/tex] are real numbers. A horizontal asymptote exists when [tex]e^{B\cdot x} \to 0[/tex], which occurs for [tex]B\cdot x \to - \infty[/tex].
For this function, the horizontal asymptote is represented by [tex]y = 0[/tex] and to change the value of the asymptote we must add the parent function by another real number ([tex]C[/tex]), that is to say:
[tex]y = A\cdot e^{B\cdot x} + C[/tex] (1)
In this case, we must use [tex]C = -3[/tex] to obtain an horizontal asymptote of -3. Thus, the right choice is: A whole number constant could have been subtracted from the exponential expression.
To learn more on asymptotes, we kindly invite to check this verified question: https://brainly.com/question/8493280
Answer: C. A whole number constant could have been added to the exponent.
Step-by-step explanation: On Edge!
Please don’t answer just for points! Help is really needed~
Answers
i dont understand
what do we need to do?
2 is 65
3 is 148
4 is 32
I am not sure at all.
Look at triangle ABC. Coordinate grid shows negative 5 to positive 5 on the x axis and y axis at intervals of 1. A triangle ABC is shown with A at ordered pair 4, 5, B at ordered pair 2, 2, and C at ordered pair 4, 2. What is the length of side AB of the triangle? (1 point) a 3 b 5 c Square root of 6 d Square root of 13
Answers
The length of side AB from the given coordinate grid is; √20
How to find the length of the side of a triangle?The formula for distance between two coordinates is;
d = √((y2 - y1)² + (x2 - x1)²)
From the graph attached in the given brainly link, we have;
A(4, 5) and B(2, 1)
Thus;
AB = √((1 - 5)² + (2 - 4)²)
AB = √(16 + 4)
AB = √20
In conclusion, the length of side AB is √20
Read more about Triangle side length at; https://brainly.com/question/3673178
#SPJ1
What is the value of the expression shown below, when p= 1 and q= 4
Answers
Answer:
The correct answer is 5.
Step-by-step explanation:
I got 100% on the assignment
PLEASE HELP!!!
46√2 simplified radical form
Answers
George and Marylin were both given the following example to complete on their
exam:
(152 +122-24x)
3.x
Below is each of their answers:
George
Marylin
(15x' +12° -24x)
3.x
(158° +12r -24x)
Зr
5r? +4x-8
5x +4x? - 8x
Which student is correct?
Explain the mistake that the other student made (Be detailed in your answer)
Answers
Answer:
this is not my level of math sorry i cant help you :(
Step-by-step explanation:
sorry
What is the answer HELP!!!!!!!!!!!!!!!!!!!!!!!!!