To construct an exponential function that expresses the population of Pottsville t years since 1980, we can use the formula:
E(t) = E₀ * (1 + r)^t
Where:
- E(t) represents the population of Pottsville t years since 1980.
- E₀ is the initial population in 1980.
- r is the annual growth rate (expressed as a decimal).
- t is the number of years since 1980.
Given that the initial population in 1980 was 36,372 people and the population in 1981 was 37,162 people, we can find the growth rate (r).
37,162 = 36,372 * (1 + r)
Divide both sides by 36,372:
(37,162 / 36,372) = 1 + r
r = (37,162 / 36,372) - 1
Now, let's calculate the growth rate:
r ≈ 0.0217
With the growth rate, we can plug it into the exponential function formula to predict the population in the year 1988 (t = 8):
E(8) = 36,372 * (1 + 0.0217)^8
E(8) ≈ 36,372 * (1.0217)^8
E(8) ≈ 36,372 * 1.1909
E(8) ≈ 43,289.172
Rounding to the nearest thousandth, the population in the year 1988 will be approximately 43,289 people.
Therefore, the correct option is not provided in the question.