HELP with this question, please.?

Question

What is the doubling period of a town whose population is increasing exponentially if it takes 20 years to grow from 750 people to 3500?

Answer 1

r = ln (3500/750)= 1.54/t
1.54/20= 0.077


doubling time is expressed as rt= ln 2 = 0.69
so
rt = 0.69
0.077t = 0.69
0.69/0.077= 8.96 years

Answer 2

9 years.

We can find the rate by the following formula:

3500=750*e^r(20)
Take natural logs:
ln(3500)=ln(750)+r(20)
ln(3500)-ln(750)=r20
1.54=20r
r=.077

This means that the population grows about 7.7% per year.
Since we want the doubling time, we set it up like this:
2=1*e^(.077t)
Solve like before. A shortcut is that the ln(2)-ln(1)=ln(2)=.693
.693=.077t
t=9 years.