Question

A town has a population of 8000 in Groves at 4.5% every year to the nearest year how long will it be until the population will reach 22,500

Answer 1

Answer:

It takes 10 years approximately for the population to reach 22,500

Step-by-step explanation:

Given:

Initial population  =  8000

Population growth rate  4.5 %

Future population = 22500

To Find:

Time taken to reach a population of  22500

Solution:

The population growth can be identified by using

$N = N_0e^{(rt)}$

where

N is  future popluation

$N_0$ is the initial population

t is the time taken

r is the rate of the growth

Here we have to find the time t, rephrasing the formula

$log(\frac{N}{N_0}) = rt$

$\frac{log(\frac{N}{N_0})}{r} = t$

Substituting the values we get,

$t = \frac{log(\frac{22,500}{ 8000})}{ 0.045}$

$t = \frac{log(2.8125)}{ 0.045}$

$t = \frac{ 0.449}{ 0.045}$

t = 9.97

t=10(approx)