Question

What is the population doubling time if population growth rate is 2% per annum?
​

Answer 1

Answer:

one present of population growth

Answer 2

The population will double given the 2% growth in 15 years.

Given :

Rate of Growth of Population = 2%

To Find :

Time in which the population doubles

Solution :

Let's initially assume that the initial population is $P_{0}$ and the time in years be 't'.

As the rate of increase is 2%, we can formulate it as :

          dP/dt = 2% of P

          $dP/dt = 2P/100$

Cross multiplying terms, we get :

          $dP/P = 2dt/100\\dP/P = dt/50$

Now, we integrate this equation to find the actual Population 'P' at any time 't' :

       $\int\limits {(1/P)} \, dP = \int\limits {dt/50} \\\\logP = (t/50) + C$

We can find the initial Population by replacing it with t = 0 i.e.

           $logP_{0} = 0/50 + C\\ C = logP_{0}$

Thus, the final equation of population P at any time t is :

          $logP = (t/50) + logP_{0}\\\\logP - logP_{0} = (t/50) \\\\log(P/P_{0}) = (t/50)\\\\ t = 50log(P/P_{0})$

So, when the Population doubles i.e. $2P_{0}$, the time taken is :

          $t = 50 * log(2P_{0} /P_{0} )\\\\t = 50 * log(2)\\\\t = 50 * (0.3)\\\\t = 15$

Hence, the Population will get double in 15 years.

To learn more about Exponential Functions, visit

https://brainly.in/question/25019459

#SPJ3