Question

1. The population of Charlotte, North Carolina, can be approximated by an exponential function. The population in Charlotte was 396,000 in 1990 and 872,000 in 2018. Create a function that finds the population of Charlotte, C in thousands t years after 1990. (1 point)

A. C(t)=872(1.029)^t
B.C(t)=396(1.029)^t
C. C(t)=872(1.202)^t
D. C(t)=396(1.045)^t

Answer 1

(B) C(t) = 396(1.029)^t.

Explanation:

We can use the formula for exponential growth to find the function that models the population of Charlotte:

C(t) = C0 * r^t

where C0 is the initial population (in thousands), r is the annual growth rate, and t is the number of years after the initial population was recorded.

We are given that the population in Charlotte was 396,000 in 1990 and 872,000 in 2018. This means that the population grew by (872,000 / 396,000)^(1/28) per year on average (since there are 28 years between 1990 and 2018).

So the annual growth rate is approximately 1.029.

Therefore, the function that finds the population of Charlotte in thousands t years after 1990 is:

C(t) = 396 * 1.029^t