Question

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?

Answer 1

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

Answer 2

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