Question

In 1975 the antique Automobile Club of America had 45,000 members it grew at an average of 4% per year through 1985. Assuming this continued what would the membership be in 2016?

Answer 1

Answer: the membership be in 2016 is 224688

Explanation:

The number of members at the club

grew at an average of 4% per year

The growth rate is exponential. We would apply the formula for exponential growth which is expressed as

A = P(1 + r/n)^ nt

Where

A represents the number of members after t years.

n represents the periodic interval at which growth is recorded.

t represents the number of years.

P represents the initial number of members.

r represents rate of growth.

From the information given,

P = 45000

r = 4% = 4/100 = 0.04

n = 1

t = 2016 - 1975 = 41

Therefore

A = 45000(1 + 0.04/1)^ 1 × 41

A = 45000(1 + 0.04/1)^41

A = 45000(1.04)^41

A = 224688

Answer 2

224,688

Explanation:

The number of members is modeled by ...

m(t) = 45000·1.04^(t-1975) . . . . where t is the year number

Then for t=2016, the membership is expected to be ...

m(2016) ≈ 45000·1.04^41 ≈ 224,688

Membership in 2016 could be estimated to be about 225,000.

___

The multiplier per year is 1+4% = 1.04. The exponent tells how many times that multiplier is repeated.