Question

Matt bought a new car at a cost of $25,000. The car depreciates approximately 15% of its value

each year.
a. What is the decay factor for the value of this car?
b. Write an equation to model the decay value of this car.
c. What will the car be worth in 10 years?

Answer 1

Part (a)

Answer: 0.85

Reason:

The car loses 15% of its value in one year. It keeps the remaining 85% (since 100-15 = 85).

The 85% then converts to the decimal form 0.85

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Part (b)

Answer: y = 25000*(0.85)^x

Reason:

The exponential equation shown in bold above is of the form

y = a*b^x

where,

• a = starting value = 25000 dollars
• b = decay factor we found previously = 0.85
• x = number of years
• y = value after x years go by

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Part (c)

Answer: $4921.86

Work Shown:

y = 25000*(0.85)^x

y = 25000*(0.85)^10

y = 25000*0.19687440434072

y = 4921.86010851808

y = 4921.86