The formula a equals A=296e^0.045t models the population

Question

The formula a equals A=296e^0.045t models the population of a particular city in thousands t years after 2011. When will the population of the city reach 444,000?

The answer should be 2020

cant seem to calculate the correct answer

Answer 1

444 = 296e^0.045t

444/296 = e^0.045t

Take the natural log of both sides and ln(e) cancels out.

ln(444/296) = 0.045t

t = ln(444/296)/0.045

t = 9

2011 + 9 = 2020

Answer 2

Our formula is :A = 296e^0.045t

We need to plug in A = 444 (it's listed as being in the thousands) and solve for t:

444/296 = e^0.045t

1.5 = e^0.045t

ln(1.5) = 0.045t

t = 9 years

Add this to the beginning year, 2011, to get your answer of 2020.