Question

A car company has found that there is a linear relationship between the money it spends on advertising and the number of cars it sells. When it spent 60000 dollars on advertising, it sold 680 cars. Moreover, for each additional 5000 dollars spent, they sold 40 more cars. Let x be the amount money they spend on advertising, in thousands of dollars. Find a formula for y, the number of cars sold.

Answer 1

The required formula for y, the number of cars sold is:
`y = 0.008x +200`.

Explanation:

Consider the provided information.

Let x represents the amount of money spend on advertising .

y is number of cars sold,

For each additional 5000 dollars spent, they sold 40 more cars.

`Slope = m = (Rise)/(Run)=(40)/(5000)=0.008`

The y-intercept form is:
`y = mx + b`

Substitute x=60,000, y=680 and m=0.008 in the above equation.

`680= 0.008(60,000)+b`

`b=680-480`

`b=200`

Thus, the required formula for y, the number of cars sold is:
`y = 0.008x +200`.