Question

(1 point) Suppose that in the year 2000, the cost of a compact car averaged $ 13000 and that in 2003, the cost averaged $ 15100. Assumingthat the relationship between yeart and cost c is linear, develop a formula for predicting the average cost of a compact car in the futuremeasuring the variable t as years since 2000. Be sure to use the lower case variables t and c.What do you predict the average cost of a compact car will be in the year 2007?

Answer 1

Variables

c: cost

t: years since 2000

Given that t is the independent variable, then the points are written (t, c)

The relation between c and t is linear. Using the slope-intercept form of a line, we get:

c = mt + b

where m is the slope and b is the y-intercept of the line

The slope of the line that passes through the points (x1, y1) and (x2, y2) is computed as follows:

`m=(y_2-y_1)/(x_2-x_1)`

In this case, the line passes through the points (0, 13000) and (3, 15100). That is, 0 years since 2000, the cost is $13000, and 3 years since 2000, the cost is $15100. Therefore, the slope of this line is:

`m=(15100-13000)/(3-0)=(2100)/(3)=700`

Given that the line passes through (0, 13000), then b = 13000. This means that the line crosses the y-axis at the value y = 13000.

Substituting m = 700 and b = 13000, the equation is:

c = 700t + 13000

Substituting t = 7 (this value corresponds to year 2007), we get:

c = 700x7 + 13000

c = 4900 + 13000

c = 17900

The average cost will be $17900 in the year 2007