Question

The table shows the number of toys sold at Penelope's Toys and Games store in different years.

Find the rate of change in the number of toys sold for each time interval. During which time
interval did the number of toys sold increase at the greatest rate?

Answer 1

The question is incomplete. Here is the complete question.

The table below shows the number of toys sold at Penelope's Toys nad Games store in different years. Find the rate of change in the number of toys sold for each time interval.

During which time interval did the number of toys sold increase at the greatest rate?

a. From 1990 to 1993

b. From 1993 to 1995

c. From 1995 to 2000

d. From 2000 to 2006

Answer: b. From 1993 to 1995

Explanation: Rate of Change is a measure of how much a quantity changed, on average, over an interval.

Generally, it is calculated as:

`rate=(\Delta y)/(\Delta x)`

or

rate = change in y / change in x

The rate of change for each time interval is calculated by

• From 1990 to 1993 ⇒ time interval of 3 years:

`rate=(32,000-20,000)/(3)`

rate = 4,000

• From 1993 to 1995 ⇒ time interval of 2 years:

`rate=(42,000-32,000)/(2)`

rate = 5,000

• From 1995 to 2000 ⇒ time interval of 5 years:

`rate=(57,000-42,000)/(5)`

rate = 3,000

• From 2000 to 2006 ⇒ time interval of 6 years:

`rate=(63,000-57,000)/(6)`

rate = 1,000

Checking all the rates of change, the one in which the number of toys sold increase at the greatest rate was between 1993 and 1995, so b is correct.