 9.3.1: Graph each exponential function. See Examples 1 through 3.y = 5x
 9.3.2: Graph each exponential function. See Examples 1 through 3.y = 4x
 9.3.3: Graph each exponential function. See Examples 1 through 3.y = 2x + 1 4
 9.3.4: Graph each exponential function. See Examples 1 through 3.y = 3x  1
 9.3.5: Graph each exponential function. See Examples 1 through 3. = a14bx
 9.3.6: Graph each exponential function. See Examples 1 through 3.y = a15bx
 9.3.7: Graph each exponential function. See Examples 1 through 3.y = a12bx 2
 9.3.8: Graph each exponential function. See Examples 1 through 3.y = a13bx+ 2
 9.3.9: Graph each exponential function. See Examples 1 through 3.y = 2x
 9.3.10: Graph each exponential function. See Examples 1 through 3.y = 3x
 9.3.11: Graph each exponential function. See Examples 1 through 3.y =  a14bx
 9.3.12: Graph each exponential function. See Examples 1 through 3.y =  a15bx
 9.3.13: Graph each exponential function. See Examples 1 through 3.f 1x2 = 2...
 9.3.14: Graph each exponential function. See Examples 1 through 3.f 1x2 = 3x1
 9.3.15: Graph each exponential function. See Examples 1 through 3.f 1x2 = 4x2
 9.3.16: Graph each exponential function. See Examples 1 through 3.f 1x2 = 2x+3
 9.3.17: Match each exponential equation with its graph below. See Examples ...
 9.3.18: Match each exponential equation with its graph below. See Examples ...
 9.3.19: Match each exponential equation with its graph below. See Examples ...
 9.3.20: Match each exponential equation with its graph below. See Examples ...
 9.3.21: Solve each equation for x. See Example 4.3x = 27
 9.3.22: Solve each equation for x. See Example 4.6x = 36
 9.3.23: Solve each equation for x. See Example 4.16x = 8
 9.3.24: Solve each equation for x. See Example 4.64x = 16
 9.3.25: Solve each equation for x. See Example 4.322x3 = 2
 9.3.26: Solve each equation for x. See Example 4.92x+1 = 81
 9.3.27: Solve each equation for x. See Example 4.14 = 23x
 9.3.28: Solve each equation for x. See Example 4.127 = 32x
 9.3.29: Solve each equation for x. See Example 4.5x = 625 3
 9.3.30: Solve each equation for x. See Example 4.2x = 64
 9.3.31: Solve each equation for x. See Example 4.4x = 8
 9.3.32: Solve each equation for x. See Example 4.32x = 4
 9.3.33: Solve each equation for x. See Example 4.27x+1 = 9
 9.3.34: Solve each equation for x. See Example 4.125x2 = 25
 9.3.35: Solve each equation for x. See Example 4.81x1 = 272x
 9.3.36: Solve each equation for x. See Example 4.43x7 = 322x
 9.3.37: Solve. Unless otherwise indicated, round results to one decimal pla...
 9.3.38: Solve. Unless otherwise indicated, round results to one decimal pla...
 9.3.39: Solve. Unless otherwise indicated, round results to one decimal pla...
 9.3.40: Solve. Unless otherwise indicated, round results to one decimal pla...
 9.3.41: Solve. Unless otherwise indicated, round results to one decimal pla...
 9.3.42: Solve. Unless otherwise indicated, round results to one decimal pla...
 9.3.43: The equation y = 136.7611.1072x gives the number of cellular phone ...
 9.3.44: The equation y = 136.7611.1072x gives the number of cellular phone ...
 9.3.45: An unusually wet spring has caused the size of the Cape Cod mosquit...
 9.3.46: The atmospheric pressure p, in pascals, on a weatherballoon decreas...
 9.3.47: Solve. Use A = Pa1 + r n b nt . Round answers to two decimal places...
 9.3.48: Solve. Use A = Pa1 + r n b nt . Round answers to two decimal places...
 9.3.49: Solve. Use A = Pa1 + r n b nt . Round answers to two decimal places...
 9.3.50: Solve. Use A = Pa1 + r n b nt . Round answers to two decimal places...
 9.3.51: Solve each equation. See Sections 2.1 and 5.8.5x  2 = 18
 9.3.52: Solve each equation. See Sections 2.1 and 5.8.3x  7 = 11
 9.3.53: Solve each equation. See Sections 2.1 and 5.8.3x  4 = 31x + 12
 9.3.54: Solve each equation. See Sections 2.1 and 5.8.2  6x = 611  x2
 9.3.55: Solve each equation. See Sections 2.1 and 5.8.x2 + 6 = 5x
 9.3.56: Solve each equation. See Sections 2.1 and 5.8.18 = 11x  x2
 9.3.57: By inspection, find the value for x that makes each statement true....
 9.3.58: By inspection, find the value for x that makes each statement true....
 9.3.59: By inspection, find the value for x that makes each statement true....
 9.3.60: By inspection, find the value for x that makes each statement true....
 9.3.61: Is the given function an exponential function? See the Concept Chec...
 9.3.62: Is the given function an exponential function? See the Concept Chec...
 9.3.63: Is the given function an exponential function? See the Concept Chec...
 9.3.64: Is the given function an exponential function? See the Concept Chec...
 9.3.65: Match each exponential function with its graph.f 1x2 = 2x
 9.3.66: Match each exponential function with its graph.f 1x2 = a12bx
 9.3.67: Match each exponential function with its graph.f 1x2 = 4x
 9.3.68: Match each exponential function with its graph.f 1x2 = a13bx
 9.3.69: Explain why the graph of an exponential function y = bx contains th...
 9.3.70: Explain why an exponential function y = bx has a yintercept of 10,...
 9.3.71: Graph.y = 0 3x 0 7
 9.3.72: Graph.y = ` a 13bx`
 9.3.73: Graph.y = 30x0
 9.3.74: Graph.y = a13b0x0
 9.3.75: Graph y = 2x and y = a 1 2 b x on the same set of axes. Describe w...
 9.3.76: Graph y = 2x and x = 2y on the same set of axes. Describe what you ...
 9.3.77: Use a graphing calculator to solve. Estimate your results to two de...
 9.3.78: Use a graphing calculator to solve. Estimate your results to two de...
 9.3.79: Use a graphing calculator to solve. Estimate your results to two de...
 9.3.80: Use a graphing calculator to solve. Estimate your results to two de...
Solutions for Chapter 9.3: Exponential Functions
Full solutions for Intermediate Algebra  6th Edition
ISBN: 9780321785046
Solutions for Chapter 9.3: Exponential Functions
Get Full SolutionsSince 80 problems in chapter 9.3: Exponential Functions have been answered, more than 67314 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Intermediate Algebra was written by and is associated to the ISBN: 9780321785046. This textbook survival guide was created for the textbook: Intermediate Algebra, edition: 6. Chapter 9.3: Exponential Functions includes 80 full stepbystep solutions.

Cyclic shift
S. Permutation with S21 = 1, S32 = 1, ... , finally SIn = 1. Its eigenvalues are the nth roots e2lrik/n of 1; eigenvectors are columns of the Fourier matrix F.

Diagonalizable matrix A.
Must have n independent eigenvectors (in the columns of S; automatic with n different eigenvalues). Then SI AS = A = eigenvalue matrix.

Fast Fourier Transform (FFT).
A factorization of the Fourier matrix Fn into e = log2 n matrices Si times a permutation. Each Si needs only nl2 multiplications, so Fnx and Fn1c can be computed with ne/2 multiplications. Revolutionary.

Free variable Xi.
Column i has no pivot in elimination. We can give the n  r free variables any values, then Ax = b determines the r pivot variables (if solvable!).

Full row rank r = m.
Independent rows, at least one solution to Ax = b, column space is all of Rm. Full rank means full column rank or full row rank.

Fundamental Theorem.
The nullspace N (A) and row space C (AT) are orthogonal complements in Rn(perpendicular from Ax = 0 with dimensions rand n  r). Applied to AT, the column space C(A) is the orthogonal complement of N(AT) in Rm.

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

Krylov subspace Kj(A, b).
The subspace spanned by b, Ab, ... , AjIb. Numerical methods approximate A I b by x j with residual b  Ax j in this subspace. A good basis for K j requires only multiplication by A at each step.

Linear transformation T.
Each vector V in the input space transforms to T (v) in the output space, and linearity requires T(cv + dw) = c T(v) + d T(w). Examples: Matrix multiplication A v, differentiation and integration in function space.

Orthogonal subspaces.
Every v in V is orthogonal to every w in W.

Permutation matrix P.
There are n! orders of 1, ... , n. The n! P 's have the rows of I in those orders. P A puts the rows of A in the same order. P is even or odd (det P = 1 or 1) based on the number of row exchanges to reach I.

Rank r (A)
= number of pivots = dimension of column space = dimension of row space.

Row picture of Ax = b.
Each equation gives a plane in Rn; the planes intersect at x.

Solvable system Ax = b.
The right side b is in the column space of A.

Sum V + W of subs paces.
Space of all (v in V) + (w in W). Direct sum: V n W = to}.

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).