Concept explainers
a.
The expression to represent the amount of money saved after w weeks.
a.
Answer to Problem 19IP
Explanation of Solution
Given:
She is saving money to buy an MP3 player that costs $212. She already saved $47 and plans to save an additional $15 per week.
Calculation:
In order to write an expression to represent the amount of money saved after w weeks, observe that she already have save $47, so it is the fixed amount and she plans to save an additional $15 every week, so an expression to represent the situation could be
Thus, the expression to represent the amount of money saved after w weeks is
So, the table can be filled using this expression as
Number of weeks | Amount of saving ($) |
1 | |
2 | |
3 | |
4 | |
b.
The line graph of the data in the table.
b.
Explanation of Solution
Given:
She is saving money to buy an MP3 player that costs $212. She already saved $47 and plans to save an additional $15 per week.
Calculation:
The plot of the data points from the table is shown below,
From the graph it is clear that she will have enough money for the MP3 player after 11th week.
c.
The number of weeks it will take her to save the money.
c.
Answer to Problem 19IP
Explanation of Solution
Given:
She is saving money to buy an MP3 player that costs $212. She already saved $47 and plans to save an additional $15 per week.
Calculation:
In order to write an expression to represent the amount of money saved after w weeks, observe that she already have save $47, so it is the fixed amount and she plans to save an additional $15 every week, so an expression to represent the situation could be
Since the cost of the MP3 player is $212, so substitute this value of A in above equation and solve for w as shown below,
So, it will take her 11 weeks to save the money to buy MP3.
d.
To compare the methods for finding the solution used in part (b) and (c).
d.
Explanation of Solution
Given:
She is saving money to buy an MP3 player that costs $212. She already saved $47 and plans to save an additional $15 per week.
Calculation:
Using the graph, once can estimate the time when she can have enough money to buy the MP3, while using the equation, one can find the exact time when she will have the required amount of money.
Chapter 8 Solutions
Glencoe Math Accelerated, Student Edition
Additional Math Textbook Solutions
A First Course in Probability (10th Edition)
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
Intro Stats, Books a la Carte Edition (5th Edition)
Calculus: Early Transcendentals (2nd Edition)
Calculus: Early Transcendentals (2nd Edition)
Elementary Statistics: Picturing the World (7th Edition)
- 1. Compute Lo F⚫dr, where and C is defined by F(x, y) = (x² + y)i + (y − x)j r(t) = (12t)i + (1 − 4t + 4t²)j from the point (1, 1) to the origin.arrow_forward2. Consider the vector force: F(x, y, z) = 2xye²i + (x²e² + y)j + (x²ye² — z)k. (A) [80%] Show that F satisfies the conditions for a conservative vector field, and find a potential function (x, y, z) for F. Remark: To find o, you must use the method explained in the lecture. (B) [20%] Use the Fundamental Theorem for Line Integrals to compute the work done by F on an object moves along any path from (0,1,2) to (2, 1, -8).arrow_forwardhelp pleasearrow_forward
- In each of Problems 1 through 4, draw a direction field for the given differential equation. Based on the direction field, determine the behavior of y as t → ∞. If this behavior depends on the initial value of y at t = 0, describe the dependency.1. y′ = 3 − 2yarrow_forwardB 2- The figure gives four points and some corresponding rays in the xy-plane. Which of the following is true? A B Angle COB is in standard position with initial ray OB and terminal ray OC. Angle COB is in standard position with initial ray OC and terminal ray OB. C Angle DOB is in standard position with initial ray OB and terminal ray OD. D Angle DOB is in standard position with initial ray OD and terminal ray OB.arrow_forwardtemperature in degrees Fahrenheit, n hours since midnight. 5. The temperature was recorded at several times during the day. Function T gives the Here is a graph for this function. To 29uis a. Describe the overall trend of temperature throughout the day. temperature (Fahrenheit) 40 50 50 60 60 70 5 10 15 20 25 time of day b. Based on the graph, did the temperature change more quickly between 10:00 a.m. and noon, or between 8:00 p.m. and 10:00 p.m.? Explain how you know. (From Unit 4, Lesson 7.) 6. Explain why this graph does not represent a function. (From Unit 4, Lesson 8.)arrow_forward
- Find the area of the shaded region. (a) 5- y 3 2- (1,4) (5,0) 1 3 4 5 6 (b) 3 y 2 Decide whether the problem can be solved using precalculus, or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution. STEP 1: Consider the figure in part (a). Since this region is simply a triangle, you may use precalculus methods to solve this part of the problem. First determine the height of the triangle and the length of the triangle's base. height 4 units units base 5 STEP 2: Compute the area of the triangle by employing a formula from precalculus, thus finding the area of the shaded region in part (a). 10 square units STEP 3: Consider the figure in part (b). Since this region is defined by a complicated curve, the problem seems to require calculus. Find an approximation of the shaded region by using a graphical approach. (Hint: Treat the shaded regi as…arrow_forwardSolve this differential equation: dy 0.05y(900 - y) dt y(0) = 2 y(t) =arrow_forwardSuppose that you are holding your toy submarine under the water. You release it and it begins to ascend. The graph models the depth of the submarine as a function of time. What is the domain and range of the function in the graph? 1- t (time) 1 2 4/5 6 7 8 -2 -3 456700 -4 -5 -6 -7 d (depth) -8 D: 00 t≤ R:arrow_forward0 5 -1 2 1 N = 1 to x = 3 Based on the graph above, estimate to one decimal place the average rate of change from x =arrow_forwardComplete the description of the piecewise function graphed below. Use interval notation to indicate the intervals. -7 -6 -5 -4 30 6 5 4 3 0 2 1 -1 5 6 + -2 -3 -5 456 -6 - { 1 if x Є f(x) = { 1 if x Є { 3 if x Єarrow_forwardComplete the description of the piecewise function graphed below. 6 5 -7-6-5-4-3-2-1 2 3 5 6 -1 -2 -3 -4 -5 { f(x) = { { -6 if -6x-2 if -2< x <1 if 1 < x <6arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- 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