please help with

Question

The city of Anville is currently home to 30000 people, and the population has been growing at a continuous rate of 7% per year. The city of Brinker is currently home to 12000 people, and the population has been growing at a continuous rate of 8% per year. In how many years will the populations of the two towns be equal?

   years

Answer 1

Growth in Anville is y =30000(e^.07t)

Brinker is y= 12000(e^.08t)

set these equal to each other and solve for t

30000(e^.07t) = 12000(e^.08t)

2.5= (e^.08t)/(e(.07t)

2.5 = e^.01t

ln 2.5 = ln e^.01t

ln2.5 = .01t

t= ln2.5.0.1= 91.6 years