A popular grows at the rate of 10% of the population per year. How long does it take for the population to doble ?

Options

A. 2 log 10 years
B. 20 log 2 years
C. 10 log 2 years
D. 5 log 2 years

Answer

C

Explanation

According to the question
`(dP)/(dt)=0/1 P`, where P is population at time t.
`therefore" "(dP)/(P) = 0.1 dt`
Integrating we get `log_(e) P = 0.1 t + c`
`{:(therefore,"Let at t = 0, P=P"_(0)),(therefore,log_(e)P_(0)=0+c),(therefore,log_(e) P = 0.1 t - log_(e)P_(0)),(therefore,log_(e)(P//P_(0))=0.1 t):}`
For double population we have
`{:(therefore,log_(e)(2P_(0)//P_(0))-0.1 t),(therefore,t=10 log_(e) 2):}`