Question

Chris bought a new motorcycle for 20000 in the year 2008. He knows that the value of the motorcycle has depreciated linearly. If the value of the motorcycle in 2012 was $19,500, what was the annual rate of change of the motorcycle’s value? Round your answer to the nearest hundredth if necessary.

Answer 1

The annual rate of change of the motorcycle's value is -$125 per year, meaning it depreciates by $125 each year.

Step-by-step explanation:

Chris bought a new motorcycle for $20,000 in the year 2008, and in 2012 its value depreciated to $19,500. To find the annual rate of change of the motorcycle's value, we use the formula for the slope of a line, which in this context represents the rate of depreciation:

Rate of change = (Change in Value) / (Change in Time)

The change in value is $19,500 - $20,000 = -$500 (negative because it's a depreciation). The change in time is 2012 - 2008 = 4 years.

Therefore, the annual rate of change = -$500 / 4 years = -$125 per year.

The negative sign indicates that the value is decreasing annually by $125.