Question

A town has a population of 2000 and grows at 4.5% every year. What will be the

population after 13 years, to the nearest whole number?

Answer 1

The population after 13 years = 3544

Explanation:

Points to remember

Compound interest

A = P[1 +R/n]^nt

Where A - amount

P - principle amount

R = rate of interest

t - number of years

n - number of times compounded yearly

Here we have to consider compounded growth.

To find the population

Here P = 2000 , R = 4.5% = 0.045% and n = 13 years

A = P[1 +R/n]^nt

= 2000[1 + 0.045/1]^(1 * 13)

= 2000 * 1.77

= 3544

Therefore the population after 13 years = 3544

Answer 2

3544

Explanation:

This is a problem of compound growth. The formula is

`F=P(1+r)^t`

Where F is the value in the future (in this case, the population after 13 years)

P is the intial amount (here, the initial population of 2000, so P = 2000)

r is the rate of growth (here, it is 4.5%, in decimal, 0.045)

t is the time frame (here, it is 13 years, so t = 13)

we can plug the numbers into the formula and solve for F:

`F=P(1+r)^t\\F=2000(1+0.045)^(13)\\F=2000(1.045)^(13)\\F=3544.4`

rounded to the nearest whole number, the population after 13 years would be 3544