The general form of exponential function ⇒⇒ [tex]a * b^x[/tex]
Where: a is the initial value and b is the rate
b > 1 ⇒⇒ exponential growth or exponential increase
b < 1 ⇒⇒ exponential decay or exponential decrease
Given: The initial population = 820
The annual rate = 23% = 0.23
The total ration between the adjacent years = 1+0.23 = 1.23
So, the exponential function to model this population is
[tex]f(x)= 820*1.23^x[/tex]
After 3 years ⇒⇒⇒ x = 3
∴ [tex]f(x) = 820 * 1.23^3 = 1,525.91[/tex] ≈ 1,526
The correct answer is:
[tex]f(x)= 820*1.23^x[/tex] ; 1,526
