Answer:
224,688
Step-by-step 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.
Answer: the membership be in 2016 is 224688
Step-by-step 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
