Question

The price of a computer component is decreasing at a rate of 15% per year.

State whether this decrease is linear or exponential. If the component costs ​$50 today, what will it cost in three​ years?

Answer 1

• exponential
• $30.71

Explanation:

Usually, this wording means the decrease is proportional to the current price, characteristic of an exponential function.

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The decay factor is 1-(decay rate), so is 1-0.15 = 0.85. After 3 years, the value has been multiplied by this factor 3 times:

$50×0.85³ ≈ $30.71 . . . . cost in 3 years

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Comment on percent per year

Less often, the indicated decrease is intended to be that percentage of the original price. The result is that the price decreases by a constant amount each year, a linear decrease. This condition most often arises in conjunction with figuring depreciation in value for tax or accounting purposes.

The upshot is that you always need to be careful to understand what the base of a percentage is intended to be.