Question

The population of a town grows at a rate proportional to the population present at time t. The initial population of 500 increases by 25% in 10 years. What will be the population in 20 years? (Round your answer to the nearest person.) persons How fast is the population growing at t20 (Round your answer to two decimal places.) persons/yr

Answer 1

The population would be 781.

The population is growing with the rate of 12.50 persons/yr.

Explanation:

Since, the formula for calculating the population, increasing with a rate per period,

`A=P(1+r)^(n)`

Where, P is the initial population,

r is the rate per period,

n is the number of period,

t is the total years,

Here, P = 500, r = 25 % = 0.25, n = 2 ( the number of '10 year period' of in 20 years is 2 )

Hence, the population in 20 years would be,

`A=500(1+0.25)^2=500(1.25)^2=781.25\approx 781`

Now, the rate of increasing per 10 year is 25 %,

⇒ The rate of increasing per year is 2.5 %,

Thus, the growing people per year = 2.5 % of 500 = 0.025 × 500 = 12.50

Hence, the population is growing at 12.50 person per year.