The following is the question.
The world population growth rate at a certain reference year was 3.5%.
Assuming exponential growth of population, after how many years, will the
population of the world would have increased by a factor 16 ?
I do not know how to start the problem. Is it the start of problem solving with equations, or something more generic? Can someone give a pointer as to how to solve this problem?
Assuming the population keeps growing at the same rate $3.5%$, it can be modeled: $$P(t)=P_0e^{0.035t} \Rightarrow P_0e^{0.035t}=16P_0 \Rightarrow t \approx 79.22.$$
$$ 1.035^n=16\rightarrow n=log_{1.035}\,16 $$
$n $ in the above has been arrived at from compound interest formula
$$P/P_0=(1+r)^n $$
Take logs to any base, getting $ \log 16/ \log 1.035=87.0816$ years.
The above is based on compound interest taken once every year. The exponential formula is a mathematical limit formula arrived at by assuming that compound interest is computed for every nanosecond! So exponentiation builds to 20 times amount in a much shorter time.
