Given the function f(x) = 2(3)^x, section a is from x = 0 to x = 1 and section b is from x = 2 to x = 3.

part a: find the average rate of change of each section.

part b: how many times greater is the average rate of change of section b than section a? explain why one rate of change is greater than the other.

i need with explanation

Average rate of change can be calculated by determining the rate of change at x = a, and at x = b

f’(x) =2 (3^x) ln(3)

f’(0) = 2 ln(3)

f’(1) = 6 ln(3)

f’(2) = 18 ln(3)

f’(3) = 54 ln(3)

Average:

at section A = [6 ln(3) – 2 ln(3)]/1 = 4 ln(3)

at section B = [54 ln(3) – 18 ln(3)]/1 = 36 ln(3)

section B is 9 times larger.

Based from the f’(x), f’(x) varies as the power of x. so the greater of value of x, the greater the rate of change.

the number of the people going.

step-by-step explanation:

the cost to buy one movie ticket is $7. if the total cost for the movie is a function of how many people go, then the input is : the number of the people going.

answer: the resulting cross section is a rectangle. solution: a plane parallel to the base of a triangular prism will intersect a cross section that is the same shape as its bases. so the cross section is a triangle.

step-by-step explanation: