Question

The population of a town was 89,443 in 1990 and then has increased at a rate of 0.6% per year since then. Which function represents the town's population t years after 1990?

Answer 1

Answer:

$f(t)=89,443(1.006^t)$

Step-by-step explanation:

In this problem we have a exponential function of the form

$f(t)=a(b^t)$

where

f(t) is the population of a town

t  is the number of years since 1990

a is the initial value

b is the base

r is the rate

b=(1+r)

we have

$a=89,443\ people\\r=0.6\%=0.6/100=0.006$

$b=1+0.006=1.006$

substitute

$f(t)=89,443(1.006^t)$