Question

The population of a town was 6575 in 2012. The population grows at a rate of 1.7 % annually.

( a ) Use the exponential growth model to write an equation that estimates the population years after 2010.

(b) Estimate the population of the town in 2025. Show your work.​

Answer 1

(a) For 2010, f(x) = 6357.024×(1 + 0.017)ˣ

(b) f(25) = 8185.93

Explanation:

The initial population of the town in 2012 = 6575

The population growth rate = 1.7%

The exponential growth model is f(x) = a(1 + r)ˣ

Where;

a = The initial value = 6575

r = The rate of growth = 1.7%

x = The number of years,

Therefore, we have;

In 2010, we have f(x) = 6575(1 + 0.017)⁻² ≈ 6357.024

Therefore, the equation becomes;

f(x) = 6357.024×(1 + 0.017)ˣ

(b) In 2025, we have;

x = 2025 - 2012 = 13 years

∴ f(x) = 6575(1 + 0.017)¹³ = 8185.93