Question

If the population is increasing exponentially at the rate of 2% per year what will be the percentage increase after 10 years

Answer 1

Given info : If the population is increasing exponentially at the rate of 2% per year.

To find : what will be the percentage increase after 10 years ?

solution : let's solve it analytical method.

r = 2%. = 2/100 = 1/50 .

so, change in population every years from 50 to 51.

percentage change in population after 10 years = [(51/50)¹⁰ - 1] × 100

= [1.21899 - 1] × 100

= 21.899 ≈ 22 %

Therefore the real percentage change is 22 % .

if you want to solve this in approximation method.

then, it can be solved easily. how ?? let's see.

we know population after n years , P = P₀(1 +r/100)ⁿ

⇒if r/100 << 1

so, ∆P/P₀ × 100 = % change in P = n × r

here n = 10 and r = 2

so, percentage change = 10 × 2 = 20 %

[note : solve approximation method only when it needed it like for competitive exam and to check options otherwise leave it. ]