The graph in the figure shows the chipmunkpopulation in a certain wilderness area

A car moves along a straight test track. The distance traveled by the car at various times is shown in the table below. Find the average speed of the car over each interval. a. 0 to 10 seconds b. 10 to 20 seconds c. 20 to 30 seconds d. 15 to 30 seconds

The yearly profit of a small manufacturing firm is shown in the tables below. What is the average rate of change of profits over the given time span? a. 19962000 b. 19962003 c. 19992002 d. 19982002

Find the average rate of change of the volume of the balloon in Example 2 as the radius increases a. from 2 to 5 inches. b. from 4 to 8 inches.

Find the average rate of change of cost for the company in Example 3 when production increases from a. 5 to 25 desks. b. 0 to 40 desks.

The graph in the figure shows the monthly sales of floral pattern ties (in thousands of ties) made by a company over a 48-month period. Sales are very low when the ties are first introduced; then they increase significantly, hold steady for a while, and then drop off as the ties go out of fashion. Find the average rate of change of sales (in ties per month) over the given interval. a. 0 to 12 b. 8 to 24 c. 12 to 24 d. 20 to 28 e. 28 to 36 f. 32 to 44 g. 36 to 40 h. 40 to 48

A certain company has found that its sales are related to the amount of advertising it does in trade magazines. The graph in the figure shows the sales (in thousands of dollars) as a function of the amount of advertising (in number of magazine ad pages). Find the average rate of change of sales when the number of ad pages increases from a. 10 to 20. b. 20 to 60. c. 60 to 100. d. 0 to 100. e. Is it worthwhile to buy more than 70 pages of ads if the cost of a one-page ad is $2000? if the cost is $5000? if the cost is $8000?

When blood flows through an artery (which can be thought of as a cylindrical tube) its velocity is greatest at the center of the artery. Because of friction along the walls of the tube, the bloods velocity decreases as the distance r from the center of the artery increases, finally becoming 0 at the wall of the artery. The velocity (in centimeters per second) is given by the functionwhere r is measured in centimeters. Find the average rate of change of the velocity as the distance from the center changes from a. to . b. to . c. to .

A car is stopped at a traffic light and begins to move forward along a straight road when the light turns green. The distance (in feet) traveled by the car in t seconds is given by for What is the average speed of the car from a. to b. to c. to d. tol.

In Exercises 914, find the average rate of change of the function f over the given interva

In Exercises 914, find the average rate of change of the function f over the given interva

In Exercises 914, find the average rate of change of the function f over the given interva

In Exercises 914, find the average rate of change of the function f over the given interva

In Exercises 914, find the average rate of change of the function f over the given interva

In Exercises 914, find the average rate of change of the function f over the given interva

In Exercises 1522, compute the difference quotient of the function.

In Exercises 1522, compute the difference quotient of the function.

In Exercises 1522, compute the difference quotient of the function.

In Exercises 1522, compute the difference quotient of the function.

In Exercises 1522, compute the difference quotient of the function.

In Exercises 1522, compute the difference quotient of the function.

In Exercises 1522, compute the difference quotient of the function.

In Exercises 1522, compute the difference quotient of the function.

Water is draining from a large tank. After t minutes there are gallons of water in the tank. a. Use the results of Exercise 19 to find the average rate at which the water runs out in the interval from 10 to 10.1 minutes. b. Do the same for the interval from 10 to 10.01 minutes. c. Estimate the rate at which the water runs out after exactly 10 minutes.

Use the results of Exercise 20 to find the average rate of change of the volume of a cube whose side has length x as x changes from a. 4 to 4.1. b. 4 to 4.01. c. 4 to 4.001. d. Estimate the rate of change of the volume at the instant when

. Use the results of Exercise 21 to find the average rate of change of the area of a circle of radius r as r changes from a. 3 to 3.5. b. 3 to 3.2. c. 3 to 3.1. d. Estimate the rate of change at the instant when e. How is your answer in part d related to the circumference of a circle of radius 3?

Under certain conditions, the volume V of a quantity of air is related to the pressure p (which is measured in kilopascals) by the equation Use the results of Exercise 22 to estimate the rate at which the volume is changing at the instant when the pressure is 50 kilopascals.

Two cars race on a straight track, beginning from a dead stop. The distance (in feet) each car has covered at each time during the first 16 seconds is shown in the figure below. a. What is the average speed of each car during this 16-second interval? b. Find an interval beginning at during which the average speed of car D was approximately the same as the average speed of car C from to c. Use secant lines and slopes to justify the statement car D traveled at a higher average speed than car C from to

The figure below shows the profits earned by a certain company during the last quarter of three consecutive years. a. Explain why the average rate of change of profits from October 1 to December 31 was the same in all three years. b. During what month in what year was the average rate of change of profits the greatest?

The graph in the figure shows the chipmunk population in a certain wilderness area. The population increases as the chipmunks reproduce, but then decreases sharply as predators move into the area. During what approximate time period (beginning on day 0) is the average growth rate of the chipmunk population positive? b. During what approximate time period, beginning on day 0, is the average growth rate of the chipmunk population 0? c. What is the average growth rate of the chipmunk population from day 50 to day 100? What does this number mean? d. What is the average growth rate from day 45 to day 50? from day 50 to day 55? What is the approximate average growth rate from day 49 to day 51?

Lucy has a viral flu. How bad she feels depends primarily on how fast her temperature is rising at that time. The figure shows her temperature during the first day of the flu. a. At what average rate does her temperature rise during the entire day? b. During what 2-hour period during the day does she feel worst? c. Find two time intervals, one in the morning and one in the afternoon, during which she feels about the same (that is, during which her temperature is rising at the same average rate).

Find the average rate of change of the function as x changes from a. to 1 b. 0 to 2

Find the average rate of change of the function as x changes from a. 3 to 0 3 to 3.5 3 to 5

Iffind the average rate of change of the composite function as x changes from 3 to 5.

If find the average rate of change of the composite function as x changes from to 1.

In Exercises 8588, find the difference quotient of the function and simplify.

In Exercises 8588, find the difference quotient of the function and simplify.g1x2 4x 1

In Exercises 8588, find the difference quotient of the function and simplify.

In Exercises 8588, find the difference quotient of the function and simplify.

The graph of the function g in the figure consists of straight line segments. Find an interval over which the average rate of change of g is a. 0 b. c. 0.5 d. Explain why the average rate of change of g is the same from to as it is from to 0. 2.5

The graph in the figure below shows the population of fruit flies during a 50-day experiment in a controlled atmosphere. a. During what 5-day period is the average rate of population growth the slowest? b. During what 10-day period is the average rate of population growth the fastest? c. Find an interval beginning at the 30th day during which the average rate of population growth is the same as the average rate from day 10 to day 20.

The profit (in hundreds of dollars) from selling x tons of an industrial chemical is given by What is the average rate of change in profit when the number of tons of the chemical sold increases from a. 4 to 8 tons? b. 4 to 5 tons? c. 4 to 4.1 tons?

On the planet Mars, the distance traveled by a falling rock (ignoring atmospheric resistance) in t seconds is feet. How far must a rock fall in order to have an average speed of 25 feet per second over that time interval?