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Concept explainers
Use a calculator with an ex key to solve Exercises 57—63. The bar graph shows the percentage of U.S. high school seniors who applied to more than three colleges for selected years from 1980 through 2013.
Source: The Higher Education Research Institute
The data in the bar graph at the bottom of the previous page can he modeled by
in which f(x) and g(x) represent the percentage of high school seniors who applied to more than three colleges x years after 1980. Use these functions to solve Exercises 57—58. Where necessary, round answers to the nearest percent.
57. a. According to the linear model, what percentage of high school seniors applied to more than three colleges in 2013?
b. According to the exponential model, what percentage of high school seniors applied to more than three colleges in 2013?
c. Which function is a better model for the data shown by the bar graph in 2013?
58. a. According to the linear model, what percentage of high school seniors applied to more than three colleges in 2010?
b. According to the exponential model, what percentage of high school seniors applied to more than three colleges in 2010?
c. Which function is a better model for the data shown by the bar graph in 2010?
59. In college, we study large volumes of information- information that, unfortunately, we do not often retain for very long. The function
describes the percentage of information, f(x), that a particular person remembers x weeks after learning the information.
a. Substitute 0 for x and, without using a calculator, find the percentage of information remembered at the moment it is first learned.
b. Substitute 1 for x and find the percentage of information that is remembered after 1 week.
c. Find the percentage of information that is remembered after 4 weeks.
d. Find the percentage of information that is remembered after one year (52 weeks).
60. In 1626. Peter Minuit persuaded the Wappinger Indians to sell him Manhattan Island for $24. If the Native Americans had put the $24 into a bank account paying 5% interest, how much would the investment have been worth in the year 2005 if interest were compounded
a. monthly?
b. continuously?
The function
models the percentage, f(x), of people x years old with some
coronary heart disease. Use this function to solve Exercises 61-62. Round answers to the nearest tenth of a percent.
61. Evaluate f(30) and describe what this means in practical terms
62. Evaluate f(70) and describe what this means in practical terms.
63. The function
describes the number of people, N(t), who become ill with influenza t weeks after its initial outbreak in a town with 30,000 inhabitants. The horizontal asymptote in the graph indicates that there is a limit to the epidemic's growth.
a. How many people became ill with the flu when the epidemic began? (When the epidemic began, t = 0.)
b. How many people were ill by the end of the third week?
c. Why can't the spread of an epidemic simply grow indefinitely? What does the horizontal asymptote shown in the graph indicate about the limiting size of the population that becomes ill?
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Chapter 12 Solutions
Introductory and Intermediate Algebra for College Students (5th Edition)
- Asked this question and got a wrong answer previously: Third, show that v3 = (−√3, −3, 3)⊤ is an eigenvector of M3 . Also here find the correspondingeigenvalue λ3 . Just from looking at M3 and its components, can you say something about the remaining twoeigenvalues? If so, what would you say?arrow_forwardDetermine whether the inverse of f(x)=x^4+2 is a function. Then, find the inverse.arrow_forwardThe 173 acellus.com StudentFunctions inter ooks 24-25/08 R Mastery Connect ac ?ClassiD-952638111# Introduction - Surface Area of Composite Figures 3 cm 3 cm 8 cm 8 cm Find the surface area of the composite figure. 2 SA = [?] cm² 7 cm REMEMBER! Exclude areas where complex shapes touch. 7 cm 12 cm 10 cm might ©2003-2025 International Academy of Science. All Rights Reserved. Enterarrow_forward
- You are given a plane Π in R3 defined by two vectors, p1 and p2, and a subspace W in R3 spanned by twovectors, w1 and w2. Your task is to project the plane Π onto the subspace W.First, answer the question of what the projection matrix is that projects onto the subspace W and how toapply it to find the desired projection. Second, approach the task in a different way by using the Gram-Schmidtmethod to find an orthonormal basis for subspace W, before then using the resulting basis vectors for theprojection. Last, compare the results obtained from both methodsarrow_forwardPlane II is spanned by the vectors: - (2) · P² - (4) P1=2 P21 3 Subspace W is spanned by the vectors: 2 W1 - (9) · 1 W2 1 = (³)arrow_forwardshow that v3 = (−√3, −3, 3)⊤ is an eigenvector of M3 . Also here find the correspondingeigenvalue λ3 . Just from looking at M3 and its components, can you say something about the remaining twoeigenvalues? If so, what would you say? find v42 so that v4 = ( 2/5, v42, 1)⊤ is an eigenvector of M4 with corresp. eigenvalue λ4 = 45arrow_forward
- Chapter 4 Quiz 2 As always, show your work. 1) FindΘgivencscΘ=1.045. 2) Find Θ given sec Θ = 4.213. 3) Find Θ given cot Θ = 0.579. Solve the following three right triangles. B 21.0 34.6° ca 52.5 4)c 26° 5) A b 6) B 84.0 a 42° barrow_forwardQ1: A: Let M and N be two subspace of finite dimension linear space X, show that if M = N then dim M = dim N but the converse need not to be true. B: Let A and B two balanced subsets of a linear space X, show that whether An B and AUB are balanced sets or nor. Q2: Answer only two A:Let M be a subset of a linear space X, show that M is a hyperplane of X iff there exists ƒ€ X'/{0} and a € F such that M = (x = x/f&x) = x}. fe B:Show that every two norms on finite dimension linear space are equivalent C: Let f be a linear function from a normed space X in to a normed space Y, show that continuous at x, E X iff for any sequence (x) in X converge to Xo then the sequence (f(x)) converge to (f(x)) in Y. Q3: A:Let M be a closed subspace of a normed space X, constract a linear space X/M as normed space B: Let A be a finite dimension subspace of a Banach space X, show that A is closed. C: Show that every finite dimension normed space is Banach space.arrow_forward• Plane II is spanned by the vectors: P12 P2 = 1 • Subspace W is spanned by the vectors: W₁ = -- () · 2 1 W2 = 0arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage