Question

PLEASE HELP! THANK YOU!

A computer was originally purchased for $900 and undergoes a 14% annual depreciation rate. The computer is now worth $364. The number of years that have passed, t, since the computer was purchased can be found using the following equation:

364 = 900(1 − 0.14)t

Solve the equation by graphing to determine how many years have passed since the computer was purchased. Round to the nearest whole year.

t = ______ years

Answer 1

answer is 6

Explanation:

Work Shown:

364 = 900(1-0.14)^t

364 = 900(0.86)^t

\frac{364}{900} = 0.86^t

\frac{91}{225} = 0.86^t

\log\left(\frac{91}{225}\right) = \log\left(0.86^t\right)

-0.39314112579027 \approx t*\log\left(0.86\right)

-0.39314112579027 \approx t*\left(-0.06550154875643\right)

\frac{-0.39314112579027}{-0.06550154875643} \approx t

6.0020126738099 \approx t

t \approx 6.0020126738099

which rounds to 6 when rounding to the nearest whole number

So it takes roughly 6 years for the value to go from $900 to $364

Answer 2

Answer is 6

------------------------------------------------------------------

Work Shown:


`364 = 900(1-0.14)^t`


`364 = 900(0.86)^t`


`(364)/(900) = 0.86^t`


`(91)/(225) = 0.86^t`


`\log\left((91)/(225)\right) = \log\left(0.86^t\right)`


`-0.39314112579027 \approx t*\log\left(0.86\right)`


`-0.39314112579027 \approx t*\left(-0.06550154875643\right)`


`(-0.39314112579027)/(-0.06550154875643) \approx t`


`6.0020126738099 \approx t`


`t \approx 6.0020126738099`

which rounds to 6 when rounding to the nearest whole number

So it takes roughly 6 years for the value to go from $900 to $364