Question

The population of a certain West Virginia city was 119,600 in 1990. By 2012, the population had become 87,050. (A) Find the exponential function of the form A (t) = Pert modeling the size of the population after t years. (use as many decimals for your rate as possible) Number t A(t) = Number e

Answer 1

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)