Question

The population of a certain town was 10,000 in the year 2000 the town manager predicted that for the next 20 years the population would be equal to p(t)=(10,000)(1.05)t where t is measured in years since 2000 according to this prediction what would be the population of the town in years 2002

Answer 1

The population of the town from 2000 to 2020 is modeled by the equation:

$p(t)=10000(1.05)^{t}$

Where t is the number of years since 2000.

We have to find the expected population of the town in 2002. The number of years from 2000 to 2002 are 2, so we have to find p(2). Replacing t by 2 in the above equation, we get:

$p(2)=10000(1.05)^{2} \\ \\ p(2)=11025$

So, according to the model, the population of town in 2002 is predicted to be 11,025.