Average Rate of Change

Question 1

The National Weather Service keeps track of the temperature for a given day in a given city. It also keeps track of this information at certain times during a given day. The following temperatures were recorded on a January day in New York City. Time of Day 10 AM 12 Noon 2 PM 4 PM 6 PM 8 PM 10 PM Temperature () 30 35 36 36 34 30 28 Determine the average rate of change (including units and sign) of temperature with respect to time over the entire twelve-hour period given in the table.

Revolt · Accepted Answer

The average rate of change of temperature with respect to time over the entire 12-hour period is approximately -0.167 degrees per hour.

Question 2

Has the marrying age of a man changed over the years? The United States Bureau of the Census takes a formal count of everyone in the U.S. every 10 years and has provided the following data that gives the median age of an American man at the time of his first marriage.Year1910192019301940195019601970198019902000Median Age25.124.624.324.322.822.823.224.726.126.8What does a rate of change of zero mean in this situation?

Revolt · Accepted Answer

The median age of a man at the time of his first marriage is, on the average, constant.

Question 3

You began membership in a new health and fitness club which has access to a dietician and personal trainer. They help you develop a special eight-week diet and exercise program. The data in the following table represents your weight, w, as a function of time, t, over an eight-week period. Time (weeks) 0 1 2 3 4 5 6 7 8 Weight (lb) 150 144 143 141 140 137 137 132 129 During which time period is the average rate of change zero?

Revolt · Accepted Answer

From week 5 to week 6

Question 4

You began membership in a new health and fitness club which has access to a dietician and personal trainer. They help you develop a special eight-week diet and exercise program. The data in the following table represents your weight, w, as a function of time, t, over an eight-week period. Time (weeks) 0 1 2 3 4 5 6 7 8 Weight (lb) 150 144 143 141 140 137 137 132 129 During which time period is the average rate of change zero?

Revolt · Accepted Answer

From week 5 to week 6

Question 5

The National Weather Service keeps track of the temperature for a given day in a given city. It also keeps track of this information at certain times during a given day. The following temperatures were recorded on a January day in New York City. Time of Day 10 AM 12 Noon 2 PM 4 PM 6 PM 8 PM 10 PM Temperature () 30 35 36 36 34 30 28 Over which period(s) of time is the average rate of change zero? What, if anything, can you conclude about the actual temperature fluctuation within this period?

Revolt · Accepted Answer

The average rate of change of temperature is 0 from 2 PM to 4 PM and also from 10 AM to 8 PM; Nothing can be concluded about the actual temperature fluctuation.

Question 6

Have vehicles gotten more fuel-efficient over the years? Between 1960 and 1999 the size and shape of automobiles in the United States has changed almost annually. The amount of fuel consumed by these vehicles has also changed. The following table describes the average fuel consumption per year per passenger car in gallons of gasoline. Year, t 1960 1970 1980 1990 1995 1997 1998 1999 Gallons Consumed Per Passenger Car 668 760 576 520 530 538 544 552 Determine the average rate of change, in gallons of gas per year, from 1995 to 1997.

Revolt · Accepted Answer

gal/year

Question 7

The National Weather Service keeps track of the temperature for a given day in a given city. It also keeps track of this information at certain times during a given day. The following temperatures were recorded on a January day in New York City. Time of Day 10 AM 12 Noon 2 PM 4 PM 6 PM 8 PM 10 PM Temperature () 30 35 36 36 34 30 28 What is the average rate of change of temperature with respect to time over the evening hours from 6 PM to 10 PM? Interpret this value in a complete sentence.

Revolt · Accepted Answer

degrees per hour; The temperature drops at an average rate of 1.5 degrees per hour from 6 PM to 10 PM.

Question 8

You began membership in a new health and fitness club which has access to a dietician and personal trainer. They help you develop a special eight-week diet and exercise program. The data in the following table represents your weight, w, as a function of time, t, over an eight-week period. Time (weeks) 0 1 2 3 4 5 6 7 8 Weight (lb) 150 144 143 141 140 137 137 132 129 Write the ratio of the change in weight for the first five weeks to the change in time for the first five weeks. Interpret the meaning of this ratio.

Revolt · Accepted Answer

, 13 pounds was lost in 5 weeks

Question 9

The results of an analysis, on the makeup of garbage, done by the Environmental Protection Agency was published in 1990. Some of the results are given in the following table, which for various years gives the number of pounds per person per day of various types of waste materials. Waste materials 1960 197019801988Glass0.200.34 0.360.28Plastics0.010.080.190.32Metals 0.320.38 0.350.34Paper0.911.191.321.60 For glass, calculate the average rate of change between 1970 and 1980. Then interpret what this value means.

Revolt · Accepted Answer

From 1970 to 1980, the number of pounds of glass per person per day increased by 0.002 per year.

Question 10

Have vehicles gotten more fuel-efficient over the years? Between 1960 and 1999 the size and shape of automobiles in the United States has changed almost annually. The amount of fuel consumed by these vehicles has also changed. The following table describes the average fuel consumption per year per passenger car in gallons of gasoline. Year, t 1960 1970 1980 1990 1995 1997 1998 1999 Gallons Consumed Per Passenger Car 668 760 576 520 530 538 544 552 Determine the average rate of change, in gallons of gas per year, from 1960 to 1990.

Revolt · Accepted Answer

gal/year

Average Rate of Change Answers

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