Answer: 17 years
Step-by-step explanation:
Exponential equation for compund amount( compunded continuously):
, where P= Principal value , r= rate of interest , t= time.
Given: A= 2P
r =4%= 0.04
To find : t
Substitute all values in the formula , we get
![2P=Pe^{0.04t}\\\\\Rightarrow\ 2=e^{0.04t}](https://tex.z-dn.net/?f=2P%3DPe%5E%7B0.04t%7D%5C%5C%5C%5C%5CRightarrow%5C%202%3De%5E%7B0.04t%7D)
Taking natural log on both sides
![\ln2=\ln e^{0.04t }\\\\\Rightarrow\ 0.693147=0.04t\\\\\Rightarrow\ t=\dfrac{ 0.693147}{0.04}\\\\\Rightarrow\ t=17.3286\approx17](https://tex.z-dn.net/?f=%5Cln2%3D%5Cln%20e%5E%7B0.04t%20%7D%5C%5C%5C%5C%5CRightarrow%5C%200.693147%3D0.04t%5C%5C%5C%5C%5CRightarrow%5C%20t%3D%5Cdfrac%7B%200.693147%7D%7B0.04%7D%5C%5C%5C%5C%5CRightarrow%5C%20t%3D17.3286%5Capprox17)
hence, it will take 17 years (approx).