Question

A town has a population of 4000 and grows at 3.5% every year. To the nearest year, how long will it be until the population will reach 7500?

Answer 1

18 years is the answer

Explanation:

Answer 2

18.273 years will take to reach the population of 7500, if a town has a population of 4000 and grows at 3.5% every year.

Explanation:

The given is,

Population of 4000

Rate of grow 3.5% every year

Population after few years 7500

Step:1

Formula to calculate the population with the grow rate every year,

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

Where,

F - Population after t years

P - Initial population

r - Rate of grow

t - No.of years

From given,

F = 7500

P = 4000

r = 3.5%

Equation becomes (1),

`7500=4000(1+0.035)^(t)`

`(7500)/(4000) = (1+0.035)^(t)`

1.875 =
`(1+0.035)^(t)`

`1.875 = (1.035)^(t)`

Take log on both sides,

`log 1.875 = (t)log 1.035`

Substitute log values,

`0.2730= (t) 0.014940349`

`t = (0.273)/(0.014940349)`

= 18.273

t = 18.273 year

or

t = 18 years 3 months 2 weeks

Result:

18.273 years will take to reach the population of 7500, if a town has a population of 4000 and grows at 3.5% every year.