Solve the given problem related to population growth A city

Solve the given problem related to population growth. A city had a population of 22,700 in 2007 and a population of 25,100 in 2012. (a) Find the exponential growth function for the city. Use t = 0 to represent 2007. (Round k to five decimal places.)

(b) Use the growth function to predict the population of the city in 2022. Round to the nearest hundred.

Solution

A city had a population of 22,700 in 2007 and a population of 25,100 in 2012

t = 0 to represent 2007.

So, P(t) = Poe^kt

Po = 22700 at t=0

So,P(t) = 22700e^kt .now find k growth constant

25100 = 22700e^(5k)

5k = 0.10053 ----> k =0.02010

a) So, P(t) = 22700e^(0.02010t)

b) in 2022 ; t=15

P(15) = 22700e^(0.02010*15)

=30687.79211

Population in the year 2022 is 30687.80