Question

The population of a town grows at the rate of 20% every 5 years. In how many year will it double itself

Answer 1

it will double itself in 10 years

Answer 2

Answer:

In 19 years the population will double itself.

Step-by-step explanation:

Rate of the population growth is given to be : 20% per 5 year

Let the current population of the town be x

So, The population after it gets double will be 2x

Now, Time after which it gets double be t years

$2x=x(\frac{120}{100})^{(\frac{t}{5})}\\\\\text{Cancelling x from both the sides}\\\\ \implies 2=(1.2)^{(\frac{t}{5})}\\\\\text{Taking log on both the sides}\\\\\implies \log 2=\frac{t}{5}\cdot\log (1.2)\\\\\implies \frac{\log 2}{\log (1.2)}=\frac{t}{5}\\\\\implies \frac{t}{5}=3.802\\\\\implies t=3.802\times 5\\\\\implies t=19.01\\\\\implies t \approx 19\text{ years}$

Therefore, In 19 years the population will double itself.