A laptop computer that costs $1150 new has a book value of $550 after 2 years. The book value is an exponential model V= ae^(kt). Find the book value of the computer after 1 year and after 3 years.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The book value of the computer that costs $1150 after 2 years is $550. Modeling the book value as V = a*e^(k*t) where a is the current price, V is the book value after t years and k is a constant gives:

550 = 1150*e^(2*k)

=> e^(2*k) = 11/23

=> 2*k = ln(11/23)

=> `k ~~ -0.3687`

To determine the book value after 1 and 3 years respectively use the value of k that has been determined and t = 1 and t = 3 in the formula V = a*e^(k*t) respectively.

The value of the computer after 1 year is $795.29 and the value after 3 years is $380.36

betpanos's profile pic

betpanos | Student | (Level 3) eNoter

Posted on

The book value of the computer that costs $1150 after 2 years is $550. Modeling the book value as V = a*e^(k*t) where a is the current price, V is the book value after t years and k is a constant gives:

550 = 1150*e^(2*k)

=> e^(2*k) = 11/23

=> 2*k = ln(11/23)

=>

To determine the book value after 1 and 3 years respectively use the value of k that has been determined and t = 1 and t = 3 in the formula V = a*e^(k*t) respectively.

The value of the computer after 1 year is $795.29 and the value after 3 years is $380.36


Thank you very much!

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