Question

a city population is growning at a rate of 3.5% per year. What is the doubling time? Bu what factor will the population increase in 50 years

Answer 1

if 3.5% is the annual rate, your job it to solve
\[(1.035)^t=2\] for \(t\)

Answer 2

takes exactly one step (and a calculator)
by the change of base formula
\[\large (1.035)^t=2\iff t=\frac{\ln(2)}{\ln(1.035)}\]

Answer 3

For rough checking purposes, the rule of 72 may be used, which says that
the doubling time is roughly 72/increase rate in %.
So the doubling time is roughly 72/3.5=20.5 years.
In 50 years, it would have doubled 2.5 times, roughly factor=4*sqrt(2)=5.6

Answer 4

good rule, that rule of 72!

Answer 5

yes, it's very handy, especially for mental calculations.