Question

The value of a car, v, in dollars, t years after it is purchased is given by v = -1,900t + 30,000. What is the slope? When will the car be worth $22,400?

Answer 1

The given equation for the value of the car is:

v = -1,900t + 30,000

The slope of this equation represents the rate at which the value of the car is decreasing over time (t). In this equation, the coefficient of t, which is -1,900, is the slope.

So, the slope is -1,900 dollars per year.

To find when the car will be worth $22,400, you can set v to 22,400 and solve for t:

22,400 = -1,900t + 30,000

Subtract 30,000 from both sides:

-7,600 = -1,900t

Now, divide both sides by -1,900 to isolate t:

t = -7,600 / -1,900 = 4

So, the car will be worth $22,400 in 4 years after it is purchased.