Liam buys a motorcycle for $2,900. Its value depreciates annually at a rate of 12%. At the end of t years, it has a value of less than $2,000. Identify whether this situation represents exponential growth or decay.

Question

Ethen Strong

Mathematics

29 December, 23:23

Liam buys a motorcycle for $2,900. Its value depreciates annually at a rate of 12%. At the end of t years, it has a value of less than $2,000. Identify whether this situation represents exponential growth or decay.

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Roberto Garrison · Answer 1

Hello!

We can first determine the equation of this this real-life situation. The initial value of $2,900 and its value depreciates annually at a rate of 12%. All percentages are out of 100, so 12% is 12/100, can in decimal form, it is 0.12.

Therefore, the exponential equation is: f (x) = 2900 (1 - 0.12) ^x. This can be simplified to f (x) = 2900 (0.88) ^x.

When the rate of change is greater than 1, then it is a exponential growth function.

When the rate of change of an exponential function is less than 1, than it is an exponential decay.

Since 0.88 is less than 1 (0.88 < 1), this situation is an exponential decay. Also, depreciation when something diminishes in value over time.

So therefore, this situation represents an exponential decay.