 4.1.1: Fill in each blank so that the resulting statement is true.The expo...
 4.1.2: Fill in each blank so that the resulting statement is true.The grap...
 4.1.3: Fill in each blank so that the resulting statement is true.The valu...
 4.1.4: Fill in each blank so that the resulting statement is true.Consider...
 4.1.5: Fill in each blank so that the resulting statement is true.If compo...
 4.1.6: In Exercises 110, approximate each number using a calculator.Round ...
 4.1.7: In Exercises 110, approximate each number using a calculator.Round ...
 4.1.8: In Exercises 110, approximate each number using a calculator.Round ...
 4.1.9: In Exercises 110, approximate each number using a calculator.Round ...
 4.1.10: In Exercises 110, approximate each number using a calculator.Round ...
 4.1.11: In Exercises 1118, graph each function by making a table ofcoordina...
 4.1.12: In Exercises 1118, graph each function by making a table ofcoordina...
 4.1.13: In Exercises 1118, graph each function by making a table ofcoordina...
 4.1.14: In Exercises 1118, graph each function by making a table ofcoordina...
 4.1.15: In Exercises 1118, graph each function by making a table ofcoordina...
 4.1.16: In Exercises 1118, graph each function by making a table ofcoordina...
 4.1.17: In Exercises 1118, graph each function by making a table ofcoordina...
 4.1.18: In Exercises 1118, graph each function by making a table ofcoordina...
 4.1.19: In Exercises 1924, the graph of an exponential function is given.Se...
 4.1.20: In Exercises 1924, the graph of an exponential function is given.Se...
 4.1.21: In Exercises 1924, the graph of an exponential function is given.Se...
 4.1.22: In Exercises 1924, the graph of an exponential function is given.Se...
 4.1.23: In Exercises 1924, the graph of an exponential function is given.Se...
 4.1.24: In Exercises 1924, the graph of an exponential function is given.Se...
 4.1.25: In Exercises 2534, begin by graphing f(x) = 2x. Then usetransformat...
 4.1.26: In Exercises 2534, begin by graphing f(x) = 2x. Then usetransformat...
 4.1.27: In Exercises 2534, begin by graphing f(x) = 2x. Then usetransformat...
 4.1.28: In Exercises 2534, begin by graphing f(x) = 2x. Then usetransformat...
 4.1.29: In Exercises 2534, begin by graphing f(x) = 2x. Then usetransformat...
 4.1.30: In Exercises 2534, begin by graphing f(x) = 2x. Then usetransformat...
 4.1.31: In Exercises 2534, begin by graphing f(x) = 2x. Then usetransformat...
 4.1.32: In Exercises 2534, begin by graphing f(x) = 2x. Then usetransformat...
 4.1.33: In Exercises 2534, begin by graphing f(x) = 2x. Then usetransformat...
 4.1.34: In Exercises 2534, begin by graphing f(x) = 2x. Then usetransformat...
 4.1.35: The figure shows the graph of f(x) = ex. In Exercises 3546, usetran...
 4.1.36: The figure shows the graph of f(x) = ex. In Exercises 3546, usetran...
 4.1.37: The figure shows the graph of f(x) = ex. In Exercises 3546, usetran...
 4.1.38: The figure shows the graph of f(x) = ex. In Exercises 3546, usetran...
 4.1.39: The figure shows the graph of f(x) = ex. In Exercises 3546, usetran...
 4.1.40: The figure shows the graph of f(x) = ex. In Exercises 3546, usetran...
 4.1.41: The figure shows the graph of f(x) = ex. In Exercises 3546, usetran...
 4.1.42: The figure shows the graph of f(x) = ex. In Exercises 3546, usetran...
 4.1.43: The figure shows the graph of f(x) = ex. In Exercises 3546, usetran...
 4.1.44: The figure shows the graph of f(x) = ex. In Exercises 3546, usetran...
 4.1.45: The figure shows the graph of f(x) = ex. In Exercises 3546, usetran...
 4.1.46: The figure shows the graph of f(x) = ex. In Exercises 3546, usetran...
 4.1.47: In Exercises 4752, graph functions f and g in the samerectangular c...
 4.1.48: In Exercises 4752, graph functions f and g in the samerectangular c...
 4.1.49: In Exercises 4752, graph functions f and g in the samerectangular c...
 4.1.50: In Exercises 4752, graph functions f and g in the samerectangular c...
 4.1.51: In Exercises 4752, graph functions f and g in the samerectangular c...
 4.1.52: In Exercises 4752, graph functions f and g in the samerectangular c...
 4.1.53: Use the compound interest formulas A = Pa1 + rn bnt andA = Pert to ...
 4.1.54: Use the compound interest formulas A = Pa1 + rn bnt andA = Pert to ...
 4.1.55: Use the compound interest formulas A = Pa1 + rn bnt andA = Pert to ...
 4.1.56: Use the compound interest formulas A = Pa1 + rn bnt andA = Pert to ...
 4.1.57: In Exercises 5758, graph f and g in the same rectangularcoordinate ...
 4.1.58: In Exercises 5758, graph f and g in the same rectangularcoordinate ...
 4.1.59: Graph y = 2x and x = 2y in the same rectangular coordinatesystem.
 4.1.60: Graph y = 3x and x = 3y in the same rectangular coordinatesystem.
 4.1.61: In Exercises 6164, give the equation of each exponential functionwh...
 4.1.62: In Exercises 6164, give the equation of each exponential functionwh...
 4.1.63: In Exercises 6164, give the equation of each exponential functionwh...
 4.1.64: In Exercises 6164, give the equation of each exponential functionwh...
 4.1.65: Use a calculator with a yx key or a key to solveExercises 6570.Indi...
 4.1.66: Use a calculator with a yx key or a key to solveExercises 6570.The ...
 4.1.67: Use a calculator with a yx key or a key to solveExercises 6570.The ...
 4.1.68: Use a calculator with a yx key or a key to solveExercises 6570.The ...
 4.1.69: Use a calculator with a yx key or a key to solveExercises 6570.The ...
 4.1.70: Use a calculator with a yx key or a key to solveExercises 6570.The ...
 4.1.71: Use a calculator with an ex key to solve Exercises 7176.The bar gra...
 4.1.72: Use a calculator with an ex key to solve Exercises 7176.The bar gra...
 4.1.73: Use a calculator with an ex key to solve Exercises 7176.The bar gra...
 4.1.74: Use a calculator with an ex key to solve Exercises 7176.The bar gra...
 4.1.75: Use a calculator with an ex key to solve Exercises 7176.The bar gra...
 4.1.76: Use a calculator with an ex key to solve Exercises 7176.The bar gra...
 4.1.77: What is an exponential function?
 4.1.78: What is the natural exponential function?
 4.1.79: Use a calculator to evaluate a1 +1xbx for x = 10, 100, 1000,10,000,...
 4.1.80: Describe how you could use the graph of f(x) = 2x to obtaina decima...
 4.1.81: You have $10,000 to invest. One bank pays 5% interestcompounded qua...
 4.1.82: a. Graph y = ex and y = 1 + x + x22 in the same viewingrectangle.b....
 4.1.83: In Exercises 8386, determine whether eachstatement makes sense or d...
 4.1.84: In Exercises 8386, determine whether eachstatement makes sense or d...
 4.1.85: In Exercises 8386, determine whether eachstatement makes sense or d...
 4.1.86: In Exercises 8386, determine whether eachstatement makes sense or d...
 4.1.87: In Exercises 8790, determine whether each statement is true orfalse...
 4.1.88: In Exercises 8790, determine whether each statement is true orfalse...
 4.1.89: In Exercises 8790, determine whether each statement is true orfalse...
 4.1.90: In Exercises 8790, determine whether each statement is true orfalse...
 4.1.91: The graphs labeled (a)(d) in the figure represent y = 3x,y = 5x, y ...
 4.1.92: Graph f(x) = 2x and its inverse function in the samerectangular coo...
 4.1.93: The hyperbolic cosine and hyperbolic sine functions aredefined byco...
 4.1.94: Solve for y: 7x + 3y = 18. (Section 1.3, Example 7)
 4.1.95: Find all zeros of f(x) = x3 + 5x2  8x + 2. (Section 3.4,Example 4)
 4.1.96: Solve and graph the solution set on a number line:2x2 + 5x 6 12. (S...
 4.1.97: Exercises 9799 will help you prepare for the material covered inthe...
 4.1.98: Exercises 9799 will help you prepare for the material covered inthe...
 4.1.99: Exercises 9799 will help you prepare for the material covered inthe...
Solutions for Chapter 4.1: Exponential Functions
Full solutions for College Algebra  7th Edition
ISBN: 9780134469164
Solutions for Chapter 4.1: Exponential Functions
Get Full SolutionsThis textbook survival guide was created for the textbook: College Algebra , edition: 7. This expansive textbook survival guide covers the following chapters and their solutions. College Algebra was written by and is associated to the ISBN: 9780134469164. Chapter 4.1: Exponential Functions includes 99 full stepbystep solutions. Since 99 problems in chapter 4.1: Exponential Functions have been answered, more than 32729 students have viewed full stepbystep solutions from this chapter.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

Column space C (A) =
space of all combinations of the columns of A.

Covariance matrix:E.
When random variables Xi have mean = average value = 0, their covariances "'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x  x) (x  x) T is positive (semi)definite; :E is diagonal if the Xi are independent.

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A

Cross product u xv in R3:
Vector perpendicular to u and v, length Ilullllvlll sin el = area of parallelogram, u x v = "determinant" of [i j k; UI U2 U3; VI V2 V3].

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.

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

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

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

Random matrix rand(n) or randn(n).
MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

Rotation matrix
R = [~ CS ] rotates the plane by () and R 1 = RT rotates back by (). Eigenvalues are eiO and eiO , eigenvectors are (1, ±i). c, s = cos (), sin ().

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

Spanning set.
Combinations of VI, ... ,Vm fill the space. The columns of A span C (A)!

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.