After 7 years the laptop computer will be worth $200 or less.
In this question, we have been given a laptop computer is purchased for $1500 . Each year, its value is 75% of its value the year before.
We need to find the number of years when laptop computer be worth $200 or less.
We can see that given situation represents exponential decay function with initial value 1500, decay rate = 0.75 and the final value = 200
We need to find period t.
For given situation we get an exponential function as,
1500 * (0.75)^t ≤ 200
(0.75)^t ≤ 2/15
t * ln(0.75) ≤ ln(2/15)
t * (-0.2877) ≤ -2.0149
t ≥ (-2.0149)/(-0.2877)
t ≥ 7
Therefore, the laptop computer will be worth $200 or less after 7 years.
Learn more about exponential function here:
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