Question

The function P(t) = 5,000(1.015)^t represents the population of the city of Springfield, where t is time in years since 2010. What does the value of P(7) mean in terms of this context?

A. Springfield has a population of 5,549 people in 2007.
B. Springfield has a population of 5,549 people i. 2017.
C. Springfield has a population of 35,525 people in 2007.
D. Springfield has a population of 35,525 people in 2017.

Answer 1

B. Springfield has a population of 5,549 people i. 2017.

Explanation:

We have the following function:

`P(t) = 5000(1.015)^(t)`

What each of these things mean?

P(t) is Springfield's population is t years after 2010.

5000 is the population after 2010.

1.015 - 1 = 0.015 is the growth rate.

t is the number of years after 2010.

P(7)

This is the population in 2010 + 7 = 2017.

So

`P(7) = 5000(1.015)^(7) = 5549`

So the correct answer is:

B. Springfield has a population of 5,549 people i. 2017.