Question

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.

Answer 1

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.