Question

An initial investment of $100 is now valued at $150. The annual interest rate is 5%, compounded continuously. The equation 100e0.05t = 150 represents the situation, where t is the number of years the money has been invested. About how long has the money been invested? Use your calculator and round to the nearest whole number.

Answer 1

8

Explanation:

edg

Answer 2

8 years

Explanation:

An initial investment of $100 is now valued at $150. The annual interest rate is 5%, compounded continuously. The equation
`100e^(0.05t) = 150` represents the situation, where t is the number of years the money has been invested.

To find out how long has the money invested we need to find out 't'

`100e^(0.05t) = 150` , solve for t

divide both sides by 100

`e^(0.05t) = 1.5`

Now to remove 'e' we take ln on both sides

`ln(e^{0.05t) = ln 1.5`

the value of
`ln(e)= 1`

`0.05t = ln 1.5`

Now divide by 0.05 on both sides

t = 8.10930

The money is invested for 8 years