Question

If the population grows at the rate of 8% per year, then the time taken for the population to be doubled, is (Given log 2 = 0.6912).

Options

• 10.27 yr

• 4.3 yr

• 6.8 yr

• 8.64 yr

Answer 1

8.64 yr

Explanation:

Let 'P' be the population at any time 't'

Given, `"dP"/"dt"` 8% of P

`=> "dP"/"P" = 8/100`dt

On integrating we get,

log P = `8/100`t + C

When, t = 0, P = P₀

⇒ C = log P₀ 

∴ `log  "P"/"P"_0 = 8/100 "t"`

When, P = 2P₀

∴ log 2 = `8/100`t

⇒ t = `100/8` log 2

= `100/8 xx 0.6912`

= 8.64 yr