In a bank principal increases at the rate of r% per year. Find the value of r if Rs. 100 double itself in 10 years `((log)_e2=0. 6931.)`

Explanation

`(dP)/(dt)=(r )/(100)*Pimplies(dP)/(P)=(r )/(100)dt`
`implies logP=(r )/(100)t+c`
Let at `t=0`, `P=P_(0)`
`:. logP_(0)=0+cimpliesc=logP_(0)`
Now, `logP=(rt)/(100)+logP_(0)`
`implies log(P)/(P_(0))=(rt)/(100)`
Given at, `t=10`, P=2P_(0)`
`:. log"(2P_(0))/(P_(0))=(r(10))/(100)=(r )/(10)=log2=0.6931`
`implies r=6.931 %`