Answer:
119,600e^(-0.0346t)
Explanation:
A) To find the exponential function of the form A(t) = Pert modeling the size of the population after t years, we need to use the given information to find the values of P and r.
We know that in 1990 (when t=0), the population was 119,600. So we have:
A(0) = 119,600
We also know that by 2012 (when t=22), the population had become 87,050. So we have:
A(22) = 87,050
Using the formula A(t) = Pert, we can write:
119,600 = Pe^(r*0)
87,050 = Pe^(r*22)
Simplifying the first equation, we get:
P = 119,600
Substituting this value into the second equation and dividing both sides by P, we get:
e^(22r) = 0.7278
Taking the natural logarithm of both sides, we get:
22r = ln(0.7278)
r = ln(0.7278)/22
r ≈ -0.0346
Therefore, the exponential function modeling the size of the population after t years is:
A(t) = 119,600e^(-0.0346t)
BOLD ANSWER: A(t) = 119,600e^(-0.0346t)