Using an exponential function, it is found that the population of the town has been growing for 2 years.
An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
In this problem, we have that the parameters are given as follows:
r = 0.15, A(0) = 20,000, A(t) = 28,000.
Hence:
[tex]A(t) = A(0)(1 + r)^t[/tex]
[tex]28000 = 20000(1.15)^t[/tex]
[tex]1.15^t = 1.4[/tex]
[tex]\log{(1.15)^t} = \log{(1.4)}[/tex]
[tex]t\log{(1.15)} = \log{(1.4)}[/tex]
[tex]t = \frac{\log{(1.4)}}{\log{(1.15)}}[/tex]
t = 2.4
Rounding to the nearest whole number, the population of the town has been growing for 2 years.
More can be learned about exponential functions at https://brainly.com/question/25537936
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