Question

During the first decade of the century, the population of a certain city was 145,380 in 2000 and 219,135 in 2010. Find the exponential growth function that models the growth of the city. Use t = 0 to represent 2000, t = 10 to represent 2010, and so on ( round k to five decimal places)

Answer 1

Answer:

The exponential growth function is $P=145380e^{0.04103t}$

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 $P=P_0 e^{kt}$

Here, P denotes total population after time t

$P_0$ denotes initial population

k denotes rate of growth

t denotes time

As $P(0)=145,380$,

$145380=P_0e^{0}\\145380=P_0\\P=145380e^{kt}$

As $P(10)=219135$

$219135=145380e^{10k}\\e^{10k}=\frac{219135}{145380}\\=1.507326\\k=\frac{1}{10}\ln (1.507326)\\=0.04103\\\Rightarrow P=145380e^{0.04103t}$