We have been given that the population of a town was 500 in 2010. The population grows at a rate of 9.6% annually.
We will use exponential growth formula to solve our given problem.
[tex]y=a\cdot (1+r)^x[/tex], where,
y = Final amount,
a = Initial value,
r = Growth rate in decimal form,
x = Time.
Let us convert 9.6% into decimal as:
[tex]9.6\%=\frac{9.6}{100}=0.096[/tex]
We can see that initial value is 500.
[tex]y=500\cdot (1+0.096)^x[/tex]
[tex]y=500\cdot (1.096)^x[/tex]
Therefore, the equation [tex]P(t)=500\cdot (1.096)^t[/tex] represents the population t years after 2010.
To find the population of the town in 2020, we will substitute [tex]t=10[/tex] in our equation as:
[tex]P(10)=500\cdot (1.096)^{10}[/tex]
[tex]P(10)=500\cdot (2.5009530650806592)[/tex]
[tex]P(10)=1250.4765325403296\approx 1250[/tex]
Therefore, the population of the town would be approximately 1250 in 2020.
