Concept explainers
a
To find the average rate of change of sales between 1993 and 2003.
a
Answer to Problem 27E
The average rate of change between 1993 and 2003 is
Explanation of Solution
Given information:
Year | Cd player sold |
1993 | 512 |
1994 | 520 |
1995 | 413 |
1996 | 410 |
1997 | 468 |
1998 | 510 |
1999 | 590 |
2000 | 607 |
2001 | 732 |
2002 | 612 |
2003 | 584 |
Formula used:
The average rate of change of the function
Calculation:
Therefore the average rate of change between 1993 and 2003 is
Hence, the average rate of change between 1993 and 2003 is
b
To find the average rate of change of sales between 1993 and 1994.
b
Answer to Problem 27E
Theaverage rate of change between 1993 and 1994 is
Explanation of Solution
Given information:
Year | Cd player sold |
1993 | 512 |
1994 | 520 |
1995 | 413 |
1996 | 410 |
1997 | 468 |
1998 | 510 |
1999 | 590 |
2000 | 607 |
2001 | 732 |
2002 | 612 |
2003 | 584 |
Formula used:
The average rate of change of the function
Calculation:
Therefore the average rate of change between 1993 and 1994 is
Hence, the average rate of change between 1993 and 1994 is
c
To find the average rate of change of sales between 1994 and 1996.
c
Answer to Problem 27E
The average rate of change between 1994 and 1996 is
Explanation of Solution
Given information:
Year | Cd player sold |
1993 | 512 |
1994 | 520 |
1995 | 413 |
1996 | 410 |
1997 | 468 |
1998 | 510 |
1999 | 590 |
2000 | 607 |
2001 | 732 |
2002 | 612 |
2003 | 584 |
Formula used:
The average rate of change of the function
Calculation:
Therefore the average rate of change between 1994 and 1996 is
Hence, the average rate of change between 1994 and 1996 is
d
To find the two successive year in which CD player sales increase and decrease most quickly
d
Answer to Problem 27E
The most increase between two successive years is between 2000-2001.
The most decease between two successive years is between 2001-2002
Explanation of Solution
Given information:
Year | Cd player sold |
1993 | 512 |
1994 | 520 |
1995 | 413 |
1996 | 410 |
1997 | 468 |
1998 | 510 |
1999 | 590 |
2000 | 607 |
2001 | 732 |
2002 | 612 |
2003 | 584 |
Formula used:
The average rate of change of the function
Calculation:
Therefore the average rate of change between 1994 and 1995 is
The average rate of change between 1995 and 1996 is
The average rate of change between 1996 and 1997 is
The average rate of change between 1997 and 1998 is
The average rate of change between 1998 and 1999 is
The average rate of change between 1999 and 2000 is
The average rate of change between 2000 and 2001 is
The average rate of change between 2001 and 2002 is
Therefore the average rate of change between 2002 and 2003 is
Hence,the most increase between two successive years is between 2000-2001 and
the most decease between two successive years is between 2001-2002
Chapter 2 Solutions
EBK PRECALCULUS: MATHEMATICS FOR CALCUL
- 2. [-/1 Points] DETAILS MY NOTES SESSCALCET2 5.5.003.MI. Evaluate the integral by making the given substitution. (Use C for the constant of integration.) x³ + 3 dx, u = x² + 3 Need Help? Read It Watch It Master It SUBMIT ANSWER 3. [-/1 Points] DETAILS MY NOTES SESSCALCET2 5.5.006.MI. Evaluate the integral by making the given substitution. (Use C for the constant of integration.) | +8 sec² (1/x³) dx, u = 1/x7 Need Help? Read It Master It SUBMIT ANSWER 4. [-/1 Points] DETAILS MY NOTES SESSCALCET2 5.5.007.MI. Evaluate the indefinite integral. (Use C for the constant of integration.) √x27 sin(x28) dxarrow_forward53,85÷1,5=arrow_forward3. In the space below, describe in what ways the function f(x) = -2√x - 3 has been transformed from the basic function √x. The graph f(x) on the coordinate plane at right. (4 points) -4 -&- -3 -- -2 4 3- 2 1- 1 0 1 2 -N -1- -2- -3- -4- 3 ++ 4arrow_forward
- 2. Suppose the graph below left is the function f(x). In the space below, describe what transformations are occuring in the transformed function 3ƒ(-2x) + 1. The graph it on the coordinate plane below right. (4 points)arrow_forward1 1. Suppose we have the function f(x) = = and then we transform it by moving it four units to the right and six units down, reflecting it horizontally, and stretching vertically by 5 units. What will the formula of our new function g(x) be? (2 points) g(x) =arrow_forwardSuppose an oil spill covers a circular area and the radius, r, increases according to the graph shown below where t represents the number of minutes since the spill was first observed. Radius (feet) 80 70 60 50 40 30 20 10 0 r 0 10 20 30 40 50 60 70 80 90 Time (minutes) (a) How large is the circular area of the spill 30 minutes after it was first observed? Give your answer in terms of π. square feet (b) If the cost to clean the oil spill is proportional to the square of the diameter of the spill, express the cost, C, as a function of the radius of the spill, r. Use a lower case k as the proportionality constant. C(r) = (c) Which of the following expressions could be used to represent the amount of time it took for the radius of the spill to increase from 20 feet to 60 feet? r(60) - r(20) Or¹(80-30) r(80) - r(30) r-1(80) - r−1(30) r-1(60) - r¹(20)arrow_forward
- 6. Graph the function f(x)=log3x. Label three points on the graph (one should be the intercept) with corresponding ordered pairs and label the asymptote with its equation. Write the domain and range of the function in interval notation. Make your graph big enough to see all important features.arrow_forwardFind the average value gave of the function g on the given interval. gave = g(x) = 8√√x, [8,64] Need Help? Read It Watch Itarrow_forward3. Mary needs to choose between two investments: One pays 5% compounded annually, and the other pays 4.9% compounded monthly. If she plans to invest $22,000 for 3 years, which investment should she choose? How much extra interest will she earn by making the better choice? For all word problems, your solution must be presented in a sentence in the context of the problem.arrow_forward
- 4 πT14 Sin (X) 3 Sin(2x) e dx 1716 S (sinx + cosx) dxarrow_forwardLet g(x) = f(t) dt, where f is the function whose graph is shown. 3 y f(t) MA t (a) At what values of x do the local maximum and minimum values of g occur? Xmin = Xmin = Xmax = Xmax = (smaller x-value) (larger x-value) (smaller x-value) (larger x-value) (b) Where does g attain its absolute maximum value? x = (c) On what interval is g concave downward? (Enter your answer using interval notation.)arrow_forward2. Graph the function f(x)=e* −1. Label three points on the graph (one should be the intercept) with corresponding ordered pairs (round to one decimal place) and label the asymptote with its equation. Write the domain and range of the function in interval notation. Make your graph big enough to see all important features. You may show the final graph only.arrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning