Question

An investment double in 10 years what was its exponential growth rate?

Answer 1

So, our rate of exponential growth is is 6.93 %

Step-by-step explanation:

The formula for exponential growth rate is

A = P
`e^(rt)` .... (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
`e^(10r)`

cancelling P on both sides

2 =
`e^(10r)`

taking natural log on both sides

ln (2) = ln (
`e^(10r)`

ln(2) = 10r(lne)

as ln(e) = 1

ln (2) = 10r

r =
`(ln(2))/(10)`

solving the natural log

r = 0.0693

or

r =6.93 %

So, our rate is 6.93 %