Question

In 2003, the price of a certain automobile was approximately $30,600 with a depreciation of $1,440 per year. After how many years will the car's value be $19,080?

a) Write an equation to model the problem. Let t represent the number of years after 2003. For example, the year 2005 would be represented by t = 2.
Answer:
b)Solve the equation to find the answer to the question above. (Note: Include the units, in this case years.)
Answer:

Answer 1

a) v(t) = 30600 -1440t

b) 8 years

Explanation:

You want an equation that models the value of a car that is initially $30,600 and falls at the rate of $1440 per year. Then you want the number of years it takes for the value to fall to $19,080.

a) Equation

Since the rate at which the value falls is a constant, we can use a linear equation for the model. Its form will be ...

value = initial value - (depreciation per year) × years

v(t) = 30,600 -1440t

b) Time

The time it takes for the value to fall to 19080 can be found by solving for t:

19080 = 30600 -1440t

1440t = 30600 -19080 = 11520

t = 11520/1440 = 8

After 8 years the car's value will be $19,080.