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

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

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wifilethbridge wifilethbridge · Answer 2 · 2019-05-21T07:16:27+02:00

Answer:

7 years

Step-by-step 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.

[tex]200 e^{0.08t} =350[/tex]

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

Solution:

[tex]200 e^{0.08t} =350[/tex]

We are supposed to find the value of t using calculator

[tex]e^{0.08t} =\frac{350}{200}[/tex]

[tex]e^{0.08t} =1.75[/tex]

[tex]t =6.995[/tex]

So, t ≈ 7 years.

Hence the money has been invested for 7 years.