Given the function h (x) = 3 (5) 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.

A.

h (x) = 3*5ˣ; h (0) = 3, h (1) = 15: rate of change is (15-3) / 1=12 (1st section)

h (2) = 3*25=75, h (3) = 3*125=375: rate of change (375-75) / 1=300 (2nd section)

b.

So the second section is 300/12=25 times greater than the first section.

The function is exponential and as x gets larger the difference between consecutive values of h (x) increases dramatically so the rate of change increases.