Answer to Question #235140 in Calculus for myka

Question

At the start of year 2015, a certain city has a population of 15,000. If the population increases by 2% every year, in how many years will the population be more than triple the original number?

Answer 1

Solution:

$P=P_0(1.02)^t$ ...(i)

Here, P = Population after t years

And $P_0$ = Initial population.

Given that $P_0=15000,P=3\times15000=45000$

We need to find t.

Putting all these values in (i).

$45000=15000(1.02)^t \\\Rightarrow3=(1.02)^t \\\Rightarrow \log 3=t \log1.02 \\\Rightarrow t=55.47$

Thus, after 56 years, the population be more than triple the original number.