Answer:
An exponential growth function is in the form of [tex]y =a(1+b)^x[/tex] where a is the initial value and b is the growth rate and is not equal to 0, b> 1.
As per the given statement: An initial population of 1,500 increases at an annual rate of 15%.
let t be the time in years.
Initial Population(a) = 1500
rate(b) = 5%
then;
[tex](1+b)^t = (1+0.15)^t = (1.15)^t[/tex] = increases 15% each year.
Then; by definition of exponential
we have an equation:
[tex]P(t)= 1500(1.15)^t[/tex] ......[1];
where 1500 represents the initial population.
Now, to find the population after 15 years.
t = 15 years
Substitute in equation [1] we get;
[tex]P(15)= 1500(1.15)^{15}[/tex]
Simplify:
P(15) =12205.5924437 population.
Therefore, the population after 15 years is, 1,2205.59(nearest hundredths) population.
