Question

Grandpa Sean started making toy drift cars to sell to hospitals to give to kids during the holidays. Below is a scatter plot to show how many drift cars he sold, starting with the first year he made them.The fifth year he made them, he sold 118 cars to hospitals all over New Jersey. Grandpa Sean was excited. In the 15th year Grandpa Sean made the cars, he sold 424. In the 22nd year, he sold 773, Create a linear model to find how many toy drift cars Grandpa Sean will probably sell in the 40th year.

Answer 1

To answer this question, we can identify the pair of values on the graph as follows:

x y

5 118

7 330

15 424

17 680

22 770

26 910

28 750

However, the values are approximated since the only given values are:

(5, 118), (15, 424), (22, 773), and we got them from the above graph.

If we use technology to find the regression line for these values, we have that:

$y=29.8135x+57.769$

And we can see this line equation as follows:

Then, to find how many toy drift cars Grandpa Sean will probably sell in the 40th year, we need to substitute the value of x = 40 into the regression line as follows:

$f(x)=29.8135x+57.769\Rightarrow f(40)=29.8135(40)+57.769$

Then, we have that:

$f(40)=1192.54+57.769\Rightarrow f(40)=1250.309$

Therefore, Grandpa Sean will probably sell, approximately, about 1250 toy drift cars in the 40th year (using all of the given values in the graph).