Suppose a population of a town is modelled by the formula P = 70(1 + 4%)^t, where P is in thousands
and t is in years since 1990. By guessing, checking, and fixing, estimate (without using logarithms) the
doubling time – the time taken for the population of the town to double. Choose a reasonable level of
accuracy. Using logarithms, find the doubling time exactly, and also to 3 significant figures.

So far I know it should be t = 33, so 70(1+4%)^33 but does this mean 4^33 then that equals that X%?

Question

Suppose a population of a town is modelled by the formula P = 70(1 + 4%)^t, where P is in thousands
and t is in years since 1990. By guessing, checking, and fixing, estimate (without using logarithms) the
doubling time – the time taken for the population of the town to double. Choose a reasonable level of
accuracy. Using logarithms, find the doubling time exactly, and also to 3 significant figures.

So far I know it should be t = 33, so 70(1+4%)^33 but does this mean 4^33 then that equals that X%?