Question

The population of Boom town is 775,000 and is increasing at a rate of6.75% each year. How many years will it take to reach a population of1,395,000?

Answer 1

If we call d = the number of years, P0= the initial population, r= increasing rate in decimal number and P(d) the population at year d, so:

$P(d)=P_0(1+r)^d$

In this case, P0 = 775,000, r=6.75%=0.0675 and P=1,395,000 so:

$\begin{gathered} 1395000=775000\cdot(1+0.0675)^d \\ \frac{1395000}{775000}=1.0675^d \\ We\text{ can take log10:} \\ \log (\frac{1395000}{775000})=\log (1.0675^d)=d\cdot\log (1.0675) \\ d=\frac{\log (\frac{1395000}{775000})}{\log (1.0675)}=8.9986\approx9 \end{gathered}$

The number of years is 9.