Question

In a bank, principal increase continuously at the rate of r% per year. Find the value of r if Rs. 100 double itself in 10 years (log_e 2=0.6931)

Answer 1

$\frac{dp}{dt}=\left(\frac{r}{100}\right)p100\frac{dp}{p}=rdt100lnp=rt+cp=e^{(\frac{rt}{100}+k)}$
at t$=$0 p$=$100
$100=e^k$
at t$=$10
$2p=200=e^{(\frac{r.10}{100}+k)}=e^{\frac{r}{10}}.e^k$
$2=e^{\frac{r}{10}}$
$log2=\frac{r}{10}r=0.6931\times 10=6.9$