Question

A city has a population of 290,000 people. Suppose that each year the population grows by 7.5%. What will the population be after 14 years? Use the calculator provided and round your answer to the nearest whole number. people x 6 ?

Answer 1

SOLUTION

This question is like a compound interest problem, where the interest rate is 7.5% compounded annually for 6 years.

Hence,

$\large A=P\left ( 1+\frac{r}{n} \right )^{nt}$

Where,

A = Final Amount

P = Initial Amount

r = Rate of interest (in decimal)

n = Number of times the interest is compounded annually

t = Time duration

Hence,

For Population Growth Model

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

Where,

P(t) = Population after t years

P0 = Initial population

r = Rate of interest (in decimal)

n = Number of times the interest is compounded annually

t = Time duration

Hence,

For this question,

P(t) = Population after 14 years = ?

P0 = Initial population = 290,00

r = Rate of interest (in decimal) = 0.075 [ 7.5% = 7.5 /100 = 0.075 ]

n = Number of times the interest is compounded annually = 1

t = Time duration = 14 years

Therefore,

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

$\large P(t)=290000\left ( 1+\frac{0.075}{1} \right )^{(1)(14)}$

$\large P(t)=290000\left ( 1+0.075 \right )^{14}$

$\large P(t)=290000\left ( 1.075 \right )^{14}$

$\large P(t)=290000\times 2.752444049$

$\large P(t)=798208.7742$

Rounded to the nearest whole number

$\large P(t)\approx798209$

Hence,

The population after 14 years should be 798209 people .