Solve the given problem related to population growth During

Solve the given problem related to population growth. During the first decade of this century, the population of a certain city grew exponentially. The population of the city was 146,230 in 2000 and 213,135 in 2010. Find the exponential growth function that models the population growth of the city. Use t = 0 to represent 2000, t = 10 to represent 2010, and so on. (Round k to five decimal places.) N(t) =

b) Use your exponential growth function to predict the population of the city in 2016. Round to the nearest thousand.

Solution

t = 0 , year 2000 , pop = 146230

t = 10 , year 2010 ,pop = 213135

P(t) = Pe^kt

213135 = 146230e^(10k)

0.37674 = 10k

k =0.03767

a) So, P(t) = 146230e^(0.03767t)

b) x = 16 , year 2016

P(16) = 146230e^(0.03767*16)

=146230*1.827 = 267162.21

= 267 thousand