Question

HELP

An initial investment of $200 is now valued at $350. The annual interest rate is 8% compounded continuously. The equation 200e^0.08t =350 represents the situation, where t is the number of years the money has been invested. About how long has the money been invested? Use a calculator and round your answer to the nearest whole number.

5 years
7 years
19 years
22 years

Answer 1

I believe it is 7 years because if you add 8% of 200 to 200 you get the fist year and then you continue adding 8% of the number you get and you count how many times you add 8% you'll get 342 after 7 times which is about 350

Answer 2

7 years

Explanation:

Given : An initial investment of $200 is now valued at $350. The annual interest rate is 8% compounded continuously.

The equation represents the situation, where t is the number of years the money has been invested.

`200 e^(0.08t) =350`

To Find : About how long has the money been invested?

Solution:

`200 e^(0.08t) =350`

We are supposed to find the value of t using calculator

`e^(0.08t) =(350)/(200)`

`e^(0.08t) =1.75`

`t =6.995`

So, t ≈ 7 years.

Hence the money has been invested for 7 years.