Answer:
So, our rate of exponential growth is is 6.93 %
Step-by-step explanation:
The formula for exponential growth rate is
A = P[tex]e^{rt}[/tex] .... (1
Here
P = is the initial investment
A = amount after certain time
As we are given after 10 years (t = 10) the investment doubles
so plugging A=2P and t= 10 into equation (1)
2P = P[tex]e^{10r}[/tex]
cancelling P on both sides
2 = [tex]e^{10r}[/tex]
taking natural log on both sides
ln (2) = ln ([tex]e^{10r}[/tex]
ln(2) = 10r(lne)
as ln(e) = 1
ln (2) = 10r
r = [tex]\frac{ln(2)}{10} [/tex]
solving the natural log
r = 0.0693
or
r =6.93 %
So, our rate is 6.93 %
