Average Rate of Change Calculus

A population of rabbits in a lab, p(x), can be modeled by the function p(x) = 20(1.014)^x, where x represents the number of days since the population was first counted. Determine, to the nearest tenth, the average rate of change from day 50 to day 100.

• 0.6

• 0.7

• 0.8

• 0.9

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

The Jamison family kept a log of the distance they traveled during a trip, as represented by the graph below. During which interval was their average speed the greatest?

• the first hour to the second hour

• the second hour to the fourth hour

• the sixth hour to the eighth hour

• the eighth hour to the tenth hour

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Firing a piece of pottery in a kiln takes place at different temperatures for different amounts of time. The graph below shows the temperatures in a kiln while firing a piece of pottery after the kiln is preheated to 200ºF. During which time interval did the temperature in the kiln show the greatest average rate of change?

• 0 to 1 hour

• 1 hour to 1.5 hours

• 2.5 hours to 5 hours

• 5 hours to 8 hours

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Voting rates in presidential elections from 1996-2012 are modeled below. Which statement does notcorrectly interpret voting rates by age based on the given graph?

• For citizens 18-29 years of age, the rate of change in voting rate was greatest between years 2000-2004.

• From 1996-2012, the average rate of change was positive for only two age groups.

• About 70% of people 45 and older voted in the 2004 election.

• The voting rates of eligible age groups lies between 35 and 75 percent during presidential elections every 4 years from 1996-2012.

Tags

CCSS.HSF.IF.B.4

Joey enlarged a 3-inch by 5-inch photograph on a copy machine. He enlarged it four times. The table below shows the area of the photograph after each enlargement. What is the average rate of change of the area from the original photograph to the fourth enlargement, to the nearest tenth?

• 4.3

• 4.5

• 5.4

• 6.0

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

The table below represents the height of a bird above the ground during flight, with P(t) representing height in feet and t representing time in seconds. Calculate the average rate of change from 3 to 9 seconds, in feet per second.

• -0.4

• -0.425

• -0.45

• -0.475

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

The table below shows the cost of mailing a postcard in different years. During which time interval did the cost increase at the greatest average rate?

• 1898-1971

• 1971-1985

• 1985-2006

• 2006-2012

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6