Question

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

Answer 1

It's the first choice, and the 't' is an exponent.

Answer 2

Answer:

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.

$= \frac{3.2}{100}$

= 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

$f(t) = 451400 (0.968)^{t}$