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 by4.7% per month. The number of VIP members is growing by 65% per year. Write a function to represent the number ofregular members after t years. Then, write an equivalent function that represents the regular members with only 1compounding per year. What is the effective yearly rate of growth of regular members? Determine the effective rate ofgrowth 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?
Accepted Solution
A:
Answer: a) 73.52% b) Regular membership is growing fasterStep-by-step 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^tThis shows the effective annual growth rate for regular members is 73.52%.__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.