Question

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

Answer 1

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

Answer 2

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