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
[tex]N = N_0e^{(rt)}[/tex]
where
N is future popluation
[tex]N_0[/tex] 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
[tex]log(\frac{N}{N_0}) = rt[/tex]
[tex]\frac{log(\frac{N}{N_0})}{r} = t[/tex]
Substituting the values we get,
[tex]t = \frac{log(\frac{22,500}{ 8000})}{ 0.045}[/tex]
[tex]t = \frac{log(2.8125)}{ 0.045}[/tex]
[tex]t = \frac{ 0.449}{ 0.045}[/tex]
t = 9.97
t=10(approx)
