Question

The American customer satisfaction index scores of McDonalds restaurants grew from 61 in 2002 to 71 in the year 2014. Find the average rate of change for the data. Show work.

Answer 1

`\large\sf{average\:rate\:of\:change= (6)/(5)\:=\:1.2}`

Explanation:

Given the American customer satisfaction index scores that increased from 61 in 2002, to 71 in 2014:

In order to solve for the average rate of change, we could simply use the average rate of change formula:

Average rate of change = Change in output/Change in input

`\huge\sf{Average\:rate\:of\:change\:=\:\frac{\triangle{y}}{\triangle{x}}\:=\:((y_2\: -\: y_1) )/((x_2\: -\: x_1))}`

Let (x₁, y₁) = (61, 2002)

(x₂, y₂) = (71, 2014)

Substitute these values into the average rate of change formula:

`\BIGG\sf{Average\:rate\:of\:change\:=\:\frac{\triangle{y}}{\triangle{x}}\:=\:((y_2\: -\: y_1) )/((x_2\: -\: x_1))\:=(2014\:-\:2002)/(71\:-\:61)\:=\:(12)/(10)\:=\:(6)/(5)}`

`\large\bf\sf{Therefore,\:the\:average\:rate\:of\:change= (6)/(5)\:=\:1.2}`.