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Solutions for Algebra and Trigonometry with Analytic Geometry | 12th Edition | ISBN: 9780495559719 | Authors: Earl Swokowski, Jeffery A. Cole

ISBN9780495559719

Solutions for Chapter 5: INVERSE, EXPONENTIAL, AND LOGARITHMIC FUNCTIONS

Solutions for Chapter 5

5.1) Is a one-to-one function?

5.2) The graph of a function f with domain is shown in the figure. Sketch the graph of .

5.3) Exer. 34: (a) Find . (b) Sketch the graphs of f and on the same coordinate plane

5.4) Exer. 34: (a) Find . (b) Sketch the graphs of f and on the same coordinate plane

5.5) Refer to the figure to determine each of the following

5.6) Suppose f and g are one-to-one functions such that , , and . Find the value, if possible.

5.7) Exer. 722: Sketch the graph of f.

5.8) Exer. 722: Sketch the graph of f.

5.9) Exer. 722: Sketch the graph of f.

5.10) Exer. 722: Sketch the graph of f.

5.11) Exer. 722: Sketch the graph of f.

5.12) Exer. 722: Sketch the graph of f.

5.13) Exer. 722: Sketch the graph of f.

5.14) Exer. 722: Sketch the graph of f.

5.15) Exer. 722: Sketch the graph of f.

5.16) Exer. 722: Sketch the graph of f.

5.17) Exer. 722: Sketch the graph of f.

5.18) Exer. 722: Sketch the graph of f.

5.19) Exer. 722: Sketch the graph of f.

5.20) Exer. 722: Sketch the graph of f.

5.21) Exer. 722: Sketch the graph of f.

5.22) Exer. 722: Sketch the graph of f.

5.23) Exer. 2324: Evaluate without using a calculator.

5.24) Exer. 2324: Evaluate without using a calculator.

5.25) Exer. 2544: Solve the equation without using a calculator.

5.26) Exer. 2544: Solve the equation without using a calculator.

5.27) Exer. 2544: Solve the equation without using a calculator.

5.28) Exer. 2544: Solve the equation without using a calculator.

5.29) Exer. 2544: Solve the equation without using a calculator.

5.30) Exer. 2544: Solve the equation without using a calculator.

5.31) Exer. 2544: Solve the equation without using a calculator.

5.32) Exer. 2544: Solve the equation without using a calculator.

5.33) Exer. 2544: Solve the equation without using a calculator.

5.34) Exer. 2544: Solve the equation without using a calculator.

5.35) Exer. 2544: Solve the equation without using a calculator.

5.36) Exer. 2544: Solve the equation without using a calculator.

5.37) Exer. 2544: Solve the equation without using a calculator.

5.38) Exer. 2544: Solve the equation without using a calculator.

5.39) Exer. 2544: Solve the equation without using a calculator.

5.40) Exer. 2544: Solve the equation without using a calculator.

5.41) Exer. 2544: Solve the equation without using a calculator.

5.42) Exer. 2544: Solve the equation without using a calculator.

5.43) Exer. 2544: Solve the equation without using a calculator.

5.44) Exer. 2544: Solve the equation without using a calculator.

5.45) Express in terms of logarithms of x, y, and z.

5.46) Express as one logarithm

5.47) Find an exponential function that has y-intercept 6 and passes through the point (1, 8).

5.48) Sketch the graph of

5.49) Exer. 4950: Use common logarithms to solve the equation for x in terms of y.

5.50) Exer. 4950: Use common logarithms to solve the equation for x in terms of y.

5.51) Exer. 5152: Approximate x to three significant figures.

5.52) Exer. 5152: Approximate x to three significant figures.

5.53) Exer. 5354: (a) Find the domain and range of the function. (b) Find the inverse of the function and its domain and ra...

5.54) Exer. 5354: (a) Find the domain and range of the function. (b) Find the inverse of the function and its domain and ra...

5.55) The number of bacteria in a certain culture at time t (in hours) is given by , where is measured in thousands. (a) Wh...

5.56) If $1000 is invested at a rate of 8% per year compounded quarterly, what is the principal after one year?

5.57) Radioactive iodine , which is frequently used in tracer studies involving the thyroid gland, decays according to , wh...

5.58) A pond is stocked with 1000 trout. Three months later, it is estimated that 600 remain. Find a formula of the form th...

5.59) Ten thousand dollars is invested in a savings fund in which interest is compounded continuously at the rate of 7% per...

5.60) In 1790, Ben Franklin left $4000 with instructions that it go to the city of Philadelphia in 200 years. It was worth ...

5.61) The current in a certain electrical circuit at time t is given by , where R is the resistance, L is the inductance, a...

5.62) The sound intensity level formula is . (a) Solve for I in terms of and . (b) Show that a one-decibel rise in the inte...

5.63) The length L of a fish is related to its age by means of the von Bertalanffy growth formula where a, b, and k are pos...

5.64) In the western United States, the area A (in ) affected by an earthquake is related to the magnitude R of the quake b...

5.65) Refer to Exercise 64. For the eastern United States, the area-magnitude formula has the form If is the area affected ...

5.66) Refer to Exercise 64. For the Rocky Mountain and Central states, the areamagnitude formula has the form If an earthqu...

5.67) Under certain conditions, the atmospheric pressure p at altitude h is given by the formula . Express h as a function ...

5.68) A rocket of mass is filled with fuel of initial mass . If frictional forces are disregarded, the total mass m of the ...

5.69) Let n be the average number of earthquakes per year that have magnitudes between R and on the Richter scale. A formul...

5.70) The energy E (in ergs) released during an earthquake of magnitude R may be approximated by using the formula (a) Solv...

5.71) A certain radioactive substance decays according to the formula , where is the initial amount of the substance and t ...

5.72) The Count Model is a formula that can be used to predict the height of preschool children. If h is height (in centime...

5.73) The current I in a certain electrical circuit at time t is given by where V is the electromotive force, R is the resi...

5.74) The technique of carbon 14 dating is used to determine the age of archaeological and geological specimens. The formul...

5.75) Based on present birth and death rates, the population of Kenya is expected to increase according to the formula , wi...

5.76) Refer to Exercise 48 of Section 5.2. If a language originally had basic words of which are still in use, then , where...

Algebra and Trigonometry with Analytic Geometry was written by and is associated to the ISBN: 9780495559719. This expansive textbook survival guide covers the following chapters and their solutions. Since 76 problems in chapter 5: INVERSE, EXPONENTIAL, AND LOGARITHMIC FUNCTIONS have been answered, more than 176846 students have viewed full step-by-step solutions from this chapter. This textbook survival guide was created for the textbook: Algebra and Trigonometry with Analytic Geometry, edition: 12. Chapter 5: INVERSE, EXPONENTIAL, AND LOGARITHMIC FUNCTIONS includes 76 full step-by-step solutions.

Key Math Terms and definitions covered in this textbook
  • Basis for V.

    Independent vectors VI, ... , v d whose linear combinations give each vector in V as v = CIVI + ... + CdVd. V has many bases, each basis gives unique c's. A vector space has many bases!

  • Cayley-Hamilton Theorem.

    peA) = det(A - AI) has peA) = zero matrix.

  • Dimension of vector space

    dim(V) = number of vectors in any basis for V.

  • Elimination matrix = Elementary matrix Eij.

    The identity matrix with an extra -eij in the i, j entry (i #- j). Then Eij A subtracts eij times row j of A from row i.

  • Elimination.

    A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

  • Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).

    Use AT for complex A.

  • Free columns of A.

    Columns without pivots; these are combinations of earlier columns.

  • Full column rank r = n.

    Independent columns, N(A) = {O}, no free variables.

  • Gauss-Jordan method.

    Invert A by row operations on [A I] to reach [I A-I].

  • Hankel matrix H.

    Constant along each antidiagonal; hij depends on i + j.

  • Hilbert matrix hilb(n).

    Entries HU = 1/(i + j -1) = Jd X i- 1 xj-1dx. Positive definite but extremely small Amin and large condition number: H is ill-conditioned.

  • Inverse matrix A-I.

    Square matrix with A-I A = I and AA-l = I. No inverse if det A = 0 and rank(A) < n and Ax = 0 for a nonzero vector x. The inverses of AB and AT are B-1 A-I and (A-I)T. Cofactor formula (A-l)ij = Cji! detA.

  • Nullspace matrix N.

    The columns of N are the n - r special solutions to As = O.

  • Orthonormal vectors q 1 , ... , q n·

    Dot products are q T q j = 0 if i =1= j and q T q i = 1. The matrix Q with these orthonormal columns has Q T Q = I. If m = n then Q T = Q -1 and q 1 ' ... , q n is an orthonormal basis for Rn : every v = L (v T q j )q j •

  • Polar decomposition A = Q H.

    Orthogonal Q times positive (semi)definite H.

  • Rayleigh quotient q (x) = X T Ax I x T x for symmetric A: Amin < q (x) < Amax.

    Those extremes are reached at the eigenvectors x for Amin(A) and Amax(A).

  • Row picture of Ax = b.

    Each equation gives a plane in Rn; the planes intersect at x.

  • Singular Value Decomposition

    (SVD) A = U:E VT = (orthogonal) ( diag)( orthogonal) First r columns of U and V are orthonormal bases of C (A) and C (AT), AVi = O'iUi with singular value O'i > O. Last columns are orthonormal bases of nullspaces.

  • Skew-symmetric matrix K.

    The transpose is -K, since Kij = -Kji. Eigenvalues are pure imaginary, eigenvectors are orthogonal, eKt is an orthogonal matrix.

  • Solvable system Ax = b.

    The right side b is in the column space of A.

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