Question

The population of a city is 451,400. The population is expected to decrease at a rate of 3.2% each year.

What function equation represents the population of the city after t years?

f(t)=451,400(0.968)tf(t)=451,400(0.968)t

f(t)=451,400(0.032)tf(t)=451,400(0.032)t

f(t)=451,400(3.2)tf(t)=451,400(3.2)t

f(t)=451,400(1.032)t

Answer 1

Find out the what function equation represents the population of the city after t years .

To prove

The population of a city is 451,400. The population is expected to decrease at a rate of 3.2% each year.

This can be represented by exponential decreasing function.

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

Where a is the initial value.

r is the rate in decimal form

t is the time.

Here

a = 451,400

3.2 % is written in the decimal form.

`= (3.2)/(100)`

= 0.032

Put in the formula

`f(t) = 451400 (1 - 0.032)^(t)`

`f(t) = 451400 (0.968)^(t)`

Therefore the decrease in the population of the city after t years is represented by

`f(t) = 451400 (0.968)^(t)`