Part A)
f(x) = 5^x
f(0) = 5^0
f(0) = 1
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f(x) = 5^x
f(1) = 5^1
f(1) = 5
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f(x) = 5^x
f(2) = 5^2
f(2) = 5*5
f(2) = 25
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f(x) = 5^x
f(3) = 5^3
f(3) = 5*5*5
f(3) = 125
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Rate of change for section A = (f(1) - f(0))/(1 - 0)
Rate of change for section A = (5 - 1)/(1 - 0)
Rate of change for section A = 4/1
Rate of change for section A = 4
Rate of change for section B = (f(3) - f(2))/(3 - 2)
Rate of change for section B = (125 - 25)/(3 - 2)
Rate of change for section B = 100/1
Rate of change for section B = 100
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Part B)
From part A) above, we found,
Rate of change for section A = 4
Rate of change for section B = 100
Which means that section B's rate of change is 25 times greater (since 100/4 = 25, or 25*4 = 100)
Answer for part B: 25
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Extra: Explain why one rate of change is greater than the other.
The rate of change for section B is larger because the exponential function is growing faster as x increases. This is shown visually by the sharper and steeper incline as the function curve goes upward. The function starts off with relatively slower growth but it accelerates in speed.
It is very important to look at all the details that are already given in the question. Only then the problem should be started for solving.
Initial population of Memphis = 350000
population of Memphis after 1 year = 406000
Then
Increase in population of Memphis in a year = 406000 - 350000
= 56000
Then
Percentage increase in the
population of Memphis in a year = (56000/350000) * 100
= (56 * 10)/35
= 560/35
= 16 percent
So there is a 16% increase in the population of Memphis in a year.
Answer:
The slope is -1/2
Step-by-step explanation:
To find the slope you have to use the formula: Δy/Δx OR change in y/change in x.
The change in y for these points is -1 (2-1)
The change in x for these points is 2 (1+2)
Then divide the change in y by the change in x. ( -1 divided by 2)
You will get -0.5 or -1/2 as your final answer for the slope.
Answer:
Step-by-step explanation:
![\int\bigg(x(x-6)^3\bigg)dx\Rightarrow\left[\begin{array}{ccc}x-6=u\\x=u+6\\dx=du\end{array}\right]\Rightarrow\int\bigg((u+6)u^3\bigg)du\\\\=\int(u^4+6u^3)du=\dfrac{1}{5}u^5+\dfrac{6}{4}u^4+C=\dfrac{1}{5}(x-6)^5+\dfrac{3}{2}(x-6)^4+C](https://tex.z-dn.net/?f=%5Cint%5Cbigg%28x%28x-6%29%5E3%5Cbigg%29dx%5CRightarrow%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx-6%3Du%5C%5Cx%3Du%2B6%5C%5Cdx%3Ddu%5Cend%7Barray%7D%5Cright%5D%5CRightarrow%5Cint%5Cbigg%28%28u%2B6%29u%5E3%5Cbigg%29du%5C%5C%5C%5C%3D%5Cint%28u%5E4%2B6u%5E3%29du%3D%5Cdfrac%7B1%7D%7B5%7Du%5E5%2B%5Cdfrac%7B6%7D%7B4%7Du%5E4%2BC%3D%5Cdfrac%7B1%7D%7B5%7D%28x-6%29%5E5%2B%5Cdfrac%7B3%7D%7B2%7D%28x-6%29%5E4%2BC)
Alan is 14. James is twice as young, meaning two times as young as his brother.
14/2 = 7
So, 7 is two times younger than Alan, who is twice as old as James.
James is 7 years old.
