Question

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

Answer 1

Answer: a) F(t) = N(1.047)^12t

b) F(t) = N(1 + 0.7352425166 )^t

c) 73.5%

Explanation:

The growing is exponential in nature.

For the number of regular members growing at 4.7% per month

R = 4.7%

t = t × 12

N = initial number of members

A function to represent the number of regular members after t years will be

F(t) = N( 1 + 4.7%)^t×12

F(t) = N(1.047)^12t

An equivalent function that represents the regular members with only 1 compounding per year.

That is, t = 1

F(t) = N(1.047)^12(1)

Then, write an equivalent function that represents the regular members with only 1 compounding per year

(1 + 0.047)^12 = 1.7352425166

F(t) = N(1 + 0.7352425166 )^t

What is the effective YEARLY rate of the growth for regular members?

(1.7352425166 - 1) * 100

yearly rate ≈ 73.5%

Answer 2

Refer below.

Explanation:

Function to represent after t years

n = x(1 + 0.047)^(t ×12)

Write an equivalent function that represents with only 1 compounded per year

(1 + 0.047)^12 = 1.7352425166

n = x(1 + 0.7352425166 )^t

The effective YEARLY rate of the growth of regular members:

(1.7352425166 - 1) ×100

Rate ≈ 73.5%