Question

Researchers estimate that a city's population will increase by 3.2% every year. The city's population in 2023 was 86,310. Write an expression for the population P(t), where t is the number of years after 2023. Write your answer in the form P(t)=a(b)t, where a and b are integers or decimals. Do not round.

Answer 1

The population growth of a city increasing annually by 3.2% with a starting population of 86,310 in 2023 is expressed as P(t) = 86,310(1.032)^t, where t is the number of years after 2023.

Step-by-step explanation:

The expression for the population P(t), where t is the number of years after 2023, based on a 3.2% annual increase, is given by the formula P(t) = a(b)^t.

In this case, a represents the initial population and b is the growth factor. Since the city's population in 2023 was 86,310, we take a = 86,310.

The growth factor b is 1 plus the growth rate expressed as a decimal, so b = 1 + 0.032 = 1.032. Therefore, the expression is P(t) = 86,310(1.032)^t.