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A new car purchased for $27,000 loses 15% of its value each year.

What is the multiplier?

Write a function of the form f(t) = abt that represents the situation.

At the current rate, what will be the value of the car in five years?

Verified Answer :

juancastillorc

multiply 27,000 x .85 (percentage of remaining value after 15% loss) raised to the 5th power (number of years) to get the answer

the value of the car in five years will be $11,980.04

frika

A new car loses 15% of its value each year, then only 85% of the car price remained. As a decimal 85% is 0.85 (if 100% is the whole 1).

Let t be the number of years when car is losing value. Then you have a regularity:

  • after first year the car's value becomes \(\$27,000\cdot 0.85=\$22,950;\)
  • after second year the car's value becomes \(\$22,950\cdot 0.85=\$19,507.5\) and so on.

Therefore, the function that represents the situation is

\(f(t)=27,000\cdot (0.85)^t.\)

When t=5, you can count that

\(f(5)=27,000\cdot (0.85)^5=11,980.0434375\approx 11,980.04.\)

Answer: coefficient - 0.85; function - \(f(t)=27,000\cdot (0.85)^t,\) value of car in five years - $11,980.04

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