Question

For a friend: a van's value depreciated linearly. The original selling price in 1990 was $36,000, and the value in 1997 was $15,000.

Find a linear function for the value V(t) of the van at the time t, where t is the number of years since the van was purchased.
a) V(t)=4500t+36000
b) V(t)=−4500t+36000
c) V(t)=−4500t−36000
d) V(t)=4500t−36000

Answer 1

To find a linear function for the value of the van at time t, use the formula y = mx + b, where m is the slope and b is the y-intercept. Calculate the slope by finding the change in value over the change in time. Apply the given values to find the linear function.

Step-by-step explanation:

To find a linear function for the value of the van at time t, we can use the formula for a linear equation in the form y = mx + b, where m is the slope and b is the y-intercept.

In this case, the van's value depreciates linearly, so we can calculate the slope by finding the change in value over the change in time.

The original selling price in 1990 was $36,000, and the value in 1997 was $15,000. Using these values, we can calculate the slope:

Slope = (Value at 1997 - Value at 1990) / (1997 - 1990)

Slope = ($15,000 - $36,000) / (1997 - 1990)

Slope = -$3,500 / 7

Slope = -$500

So, the linear function for the value V(t) of the van at the time t is:

V(t) = -$500t + $36,000