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

The function that represents the town's population t years after 1990 is P(t) = 89443 * (1 + 0.006)^t. This formula applies the growth rate of 0.6% per year to the initial population in 1990.

Step-by-step explanation:

To find the function that represents the town's population t years after 1990, we need to start with the initial population in 1990 and apply the growth rate of 0.6% per year. The function would be:

P(t) = 89443 * (1 + 0.006)^t

Where:

• P(t) represents the population t years after 1990
• 89443 is the initial population in 1990
• 0.006 is the growth rate per year (0.6%) expressed as a decimal
• t is the number of years after 1990

For example, to find the population in the year 2000 (10 years after 1990), we would substitute t = 10 into the function:

P(10) = 89443 * (1 + 0.006)^10

Calculating this gives us:

P(10) = 89443 * (1.006)^10 ≈ 97,114

So, the population in the year 2000 would be approximately 97,114.

Answer 2

`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)`