Question

ALGEBRA 2 HELP PLEASE

Robyn brought a laptop for $1,5000. It will depreciate 15% each year that she owns it.

a. A student writes an explicit formula to represent the value of the computer after n years below. What is the student's error? Explain.


`a_n=$1,5000(.15)^(n-1)`

b. Use your correct explicit formula from Part A above to find the value of the laptop at the beginning of the 4th year. (Please show work)

Answer 1

Part (a)

The error is that the 0.15 should be 0.85 because 1-0.15 = 0.85

If the laptop loses 15% of its value, then it keeps the remaining 85%.

Therefore, the formula should be
`a_n = 1500(0.85)^(n-1)`

I'm assuming the "$1,5000" should have been "$1,500".

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Part (b)

Plug n = 4 into the formula.

`a_n = 1500(0.85)^(n-1)\\\\a_4 = 1500(0.85)^(4-1)\\\\a_4 = 1500(0.85)^(3)\\\\a_4 = 1500(0.614125)\\\\a_4 = 921.1875\\\\a_4 \approx 921.19\\\\`

The laptop's value is approximately $921.19 at the beginning of the 4th year.