Question

The table below shows the population of a town over x years.

A 2-column table with 5 rows. The first column is labeled years with entries 0, 5, 10, 15, 20. The second column is labeled population with entries 10,500; 16,000; 26,000; 40,000; 65,000.
What values, rounded to the nearest tenth, complete the exponential regression equation that models the data?

f(x) =
(
)x
Based on the regression equation and rounded to the nearest whole person, what is the estimated population after 25 years?

people

Answer 1

First, an exponential fit gives
ln(f(x)) ≈ 9.2444 + 0.091246 x,
so
f(x) ≈ 10346.0·e^(0.091246x) = 10346.0·(1.09554)^x.

Rounded to the nearest tenth the parameters are: a ≈ 10346.0 and base ≈ 1.1 (more precisely 1.0955).

Using the regression model, the estimated population at 25 years is about 101,255 people (rounded to the nearest whole person).