Question

The population of a city can be modeled using the formula p=100,000e0.04t
, where t is the number of years after 2012
and P is the city's population. Which of the following equations can be used to find the number of years after 2012
that the population will become 250,000
?

Answer 1

Set p = 250,000: 250,000 = 100,000 e^{0.04t}.
Divide by 100,000: 2.5 = e^{0.04t}.
Take ln: ln(2.5) = 0.04t, so t = ln(2.5)/0.04 ≈ 22.9 years (about year 2012 + 22.9 ≈ 2035).