Question

Directions: Answer the questions below. Make sure to show your work and justify all your answers.

15. The city bike rental program is analyzing their growth in member rates. The number of regular members is growing by
4.7% per month. The number of VIP members is growing by 65% per year. Write a function to represent the number of
regular members after t years. Then, write an equivalent function that represents the regular members with only 1
compounding per year. What is the effective yearly rate of growth of regular members? Determine the effective rate of
growth per year for regular members. Which type of member is growing at a faster rate?
a What is the effective YEARLY rate of the growth for regular members?
b. Which type of member is growing at a faster rate?

Answer 1

a) 73.52%

b) Regular membership is growing faster

Explanation:

a) r(t) = r0·1.047^(12t) . . . . regular members after t years, where r0 is the initial value of regular members at t=0.

Equivalently, this is ...

r(t) = r0·(1.047^12)^t ≈ r0·1.7352^t

This shows the effective annual growth rate for regular members is 73.52%.

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b) The 74% yearly growth rate of regular members is higher than the 65% yearly growth rate of VIP members. Regular membership is growing faster.