The last one is the answer.......
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.
Answer:
Step-by-step explanation:
Translating to English:
A cylinder has a volume that is 25% greater than a sphere with a surface area of . What is the cylinder's volume?
<u>Solution:</u>
This isn't a hard question. You do not need to get inside the nitty gritty of the formula for volumes and surface areas. The SA of sphere is given and we are told the VOLUME of CYLINDER is 25% GREATER THAN THIS!
So, we just need to figure out what is 25% greater than
Lets keep the as constant and find 25% greater than 576 and we tag along the .
We need to find 25% of 576 and add it to 576 to get our answer.
25% = 25/100 = 0.25
So,
0.25*576 = 144
So,
144 + 576 = 720
The answer would be
The 2nd answer choice (with a typo here), is correct.