Question

13. The population of a city is currently 45,000 and is declining at a rate of 2% each year. Estimate the population after a period of 5 years. Use the formula ƒ(t) = aert.

Answer 1

40,718

Step-by-step ex

The population of a city is currently 45,000 and is declining at a rate of 2% each year. Estimate the population after a period of 5 years. Use the formula ƒ(t) = aert. planation:

Answer 2

Given:

Initial population = 45,000

Decreasing rate = 2%

Time = 5 year

To find:

The population after a period of 5 years.

Solution:

Formula used:

`f(t)=ae^(rt)`

where, a is initial population, r is rate and t is time.

`r=(2)/(100)=0.02`

Decreasing rate represented by -0.02.

Substitute a=45000, r=-0.02 and t=5 in the above formula.

`f(5)=45000e^(-0.02(5))`

`f(5)=45000e^(-0.1)`

`f(5)=45000(0.904837418)`

`f(5)=40717.68381`

Approximate the value to the previous integer.

`f(5)\approx 40717`

Therefore, the population after 5 years is 40717.