Question

Suppose a city with population300,000 has been growing at a rate of3% per year. If this rate continues, find the population of this city in22 years. Part 1The population in22 years will be approximatelyenter your response here. (Round to the nearest whole number as needed.)

Answer 1

We are given

Initial Population = 300,000

Rate of increasing per year = 3% = 0.03

We want to find the population at time t = 22 years

Solution

The formula to use the formula for the compound interest given as

$P(t)=P_0(1+\frac{r}{n})^{nt}$

Here

$\begin{gathered} P(t)=\text{Population at any given time} \\ P_0=\text{initial population} \\ r=\text{rate } \\ n=number\text{ of times of increment in a year} \\ t=\text{time} \end{gathered}$

Thus, we want to find P(22)

$\begin{gathered} P_0=300,000 \\ r=0.03 \\ n=1 \\ t=22 \end{gathered}$

Substituting into the formula we have

$\begin{gathered} P(t)=P_0(1+\frac{r}{n})^{nt} \\ P(22)=300000(1+\frac{0.03}{1})^{22} \\ P(22)=300000(1.03)^{22} \\ P(22)=574831.0227 \\ P(22)=574831\text{ (to the nearest whole number)} \end{gathered}$

Therefore, the population in 22 years time will be 574,831