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

Answer:

8

Step-by-step explanation:

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Answer 2

Answer:

8 years

Step-by-step 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