Question

Please help me with this problem about growth and decay.

Answer 1

The population of the town in Iowa after 13 years is 9,130

Explanation:

The given parameters of the town are;

The population of the town in Iowa in 2007, a = 12,355

The rate at which the people of the town leave Iowa for Minnesota, r = 2.3% per year

We are required to find the population of the town after t = 13 years

The given population decay function is presented as follows;

`f(t) = a \cdot (1 - r)^t`

Where;

a = The initial population of the town = 12,355

r = The annual percentage rate at which the people of the town leave Iowa for Minnesota = 2.3% per year = 0.023

t = The number of years over which the population changes = 13 years = 13

∴ f(13) = 12,355 × (1 - 0.023)¹³ = 9130.02734094

Therefore, the population of the town in Iowa after 13 years ≈ 9,130 (we round down to the nearest whole number).