Answered

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

Verified Answer :

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

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



Answer:

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

Step-by-step explanation:

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