Math help I know the formula but can’’t figure out how to put it in the calculator this is honestly like a foreign language to me

Question

the initial population of a town is 3,200 and it grows with a doubling time of 10 years what will the population be in 8 years

Answer 1

One model of population growth for a town is this:

P = P_o e^rt

where P_o = initial population

r = rate of growth (percentage rate, expressed as a decimal)

t = time (say years)

So the model applied to this problem (thus far) is:

P = 3200 e^rt

If the population doubles in 10 years then that gives enough information to solve for the rate r:

6400 = 3200 e^r*10

2 = e^r*10

ln(2) = 10r

r = ln(2) / 10 or approximately 0.0693 (6.93% per year)

Now the model looks like this:

P = 3200*e^0.0693*t

You can now plug t = 8 into a calculator. I get 5571 when rounding up to nearest integer.

There are other models that might apply to a population of a town, the one I've given you is one of the simplest.