Question

if population of a country increased by 2% per year .after 35 years it will become double than after how much time it will be 10 times of initial

Answer 1

Answer:

Hence, the number of years after which the population of country becomes 10 times the initial is 116.3 years.

Step-by-step explanation:

It is given that:

if population of a country increased by 2% per year .

Then Let $P_0$ denote the initial population then the population of a country can be modeled by the function: P(t) as:

$P(t)=P_0(1+0.2)^t$

Now we are asked to find the value of t given that the $P(t)=10\times P_0$

Hence, we have:

$P_0(1+0.2)^t=10P_0\\\\(1.02)^t=10$

On, taking logarithmic function we have:

$t\log (1.02)=\log (10)$

since, we have the property of logarithmic function as:

$\log m^n=n\log m$

$t\log (1.02)=1\\\\t=\dfrac{1}{\log (1.02)}$

Hence, on solving we obtain:

t=116.3 years.

Hence, the number of years after which the population of country becomes 10 times the initial is 116.3 years.