Answer:
The exponential growth function is [tex]P=145380e^{0.04103t}[/tex]
Step-by-step explanation:
Given: The population of a certain city was 145,380 in 2000 and 219,135 in 2010.
To find: exponential growth function that models the growth of the city
Solution:
The exponential growth function is given by [tex]P=P_0 e^{kt}[/tex]
Here, P denotes total population after time t
[tex]P_0[/tex] denotes initial population
k denotes rate of growth
t denotes time
As [tex]P(0)=145,380[/tex],
[tex]145380=P_0e^{0}\\145380=P_0\\P=145380e^{kt}[/tex]
As [tex]P(10)=219135[/tex]
[tex]219135=145380e^{10k}\\e^{10k}=\frac{219135}{145380}\\=1.507326\\k=\frac{1}{10}\ln (1.507326)\\=0.04103\\\Rightarrow P=145380e^{0.04103t}[/tex]
