 6.3.1: 2 8 = 2>3 4
 6.3.2: Solve x2 + 3x = 4
 6.3.3: True or False To graph shift the graph of y = x to the left 2 units
 6.3.4: Find the average rate of change of from to
 6.3.5: True or False The function has as a horizontal asymptote
 6.3.6: A(n) is a function of the form and are real numbers. The base a is ...
 6.3.7: For an exponential function f1x + 12 f1x2 f
 6.3.8: True or False The domain of the exponential function , is the set o...
 6.3.9: True or False The range of the exponential function , is the set of...
 6.3.10: True or False The graph of the exponential function , has no xinte...
 6.3.11: The graph of every exponential function and , passes through three ...
 6.3.12: If the graph of the exponential function where , is decreasing, the...
 6.3.13: If , then .
 6.3.14: True or False The graphs of and are identical.
 6.3.15: In 1524, approximate each number using a calculator. Express your a...
 6.3.16: In 1524, approximate each number using a calculator. Express your a...
 6.3.17: In 1524, approximate each number using a calculator. Express your a...
 6.3.18: In 1524, approximate each number using a calculator. Express your a...
 6.3.19: In 1524, approximate each number using a calculator. Express your a...
 6.3.20: In 1524, approximate each number using a calculator. Express your a...
 6.3.21: In 1524, approximate each number using a calculator. Express your a...
 6.3.22: In 1524, approximate each number using a calculator. Express your a...
 6.3.23: In 1524, approximate each number using a calculator. Express your a...
 6.3.24: In 1524, approximate each number using a calculator. Express your a...
 6.3.25: n 2532, determine whether the given function is linear, exponential...
 6.3.26: n 2532, determine whether the given function is linear, exponential...
 6.3.27: n 2532, determine whether the given function is linear, exponential...
 6.3.28: n 2532, determine whether the given function is linear, exponential...
 6.3.29: n 2532, determine whether the given function is linear, exponential...
 6.3.30: n 2532, determine whether the given function is linear, exponential...
 6.3.31: n 2532, determine whether the given function is linear, exponential...
 6.3.32: n 2532, determine whether the given function is linear, exponential...
 6.3.33: In 3340, the graph of an exponential function is given. Match each ...
 6.3.34: In 3340, the graph of an exponential function is given. Match each ...
 6.3.35: In 3340, the graph of an exponential function is given. Match each ...
 6.3.36: In 3340, the graph of an exponential function is given. Match each ...
 6.3.37: In 3340, the graph of an exponential function is given. Match each ...
 6.3.38: In 3340, the graph of an exponential function is given. Match each ...
 6.3.39: In 3340, the graph of an exponential function is given. Match each ...
 6.3.40: In 3340, the graph of an exponential function is given. Match each ...
 6.3.41: In 4152, use transformations to graph each function. Determine the ...
 6.3.42: In 4152, use transformations to graph each function. Determine the ...
 6.3.43: In 4152, use transformations to graph each function. Determine the ...
 6.3.44: In 4152, use transformations to graph each function. Determine the ...
 6.3.45: In 4152, use transformations to graph each function. Determine the ...
 6.3.46: In 4152, use transformations to graph each function. Determine the ...
 6.3.47: In 4152, use transformations to graph each function. Determine the ...
 6.3.48: In 4152, use transformations to graph each function. Determine the ...
 6.3.49: In 4152, use transformations to graph each function. Determine the ...
 6.3.50: In 4152, use transformations to graph each function. Determine the ...
 6.3.51: In 4152, use transformations to graph each function. Determine the ...
 6.3.52: In 4152, use transformations to graph each function. Determine the ...
 6.3.53: In 5360, begin with the graph of [Figure 27] and use transformation...
 6.3.54: In 5360, begin with the graph of [Figure 27] and use transformation...
 6.3.55: In 5360, begin with the graph of [Figure 27] and use transformation...
 6.3.56: In 5360, begin with the graph of [Figure 27] and use transformation...
 6.3.57: In 5360, begin with the graph of [Figure 27] and use transformation...
 6.3.58: In 5360, begin with the graph of [Figure 27] and use transformation...
 6.3.59: In 5360, begin with the graph of [Figure 27] and use transformation...
 6.3.60: In 5360, begin with the graph of [Figure 27] and use transformation...
 6.3.61: In 6180, solve each equation. 7x = 73
 6.3.62: In 6180, solve each equation. 5x = 56
 6.3.63: In 6180, solve each equation. 2x = 16
 6.3.64: In 6180, solve each equation. 3x = 81
 6.3.65: In 6180, solve each equation. a15bx= 125
 6.3.66: In 6180, solve each equation. a4bx= 164
 6.3.67: In 6180, solve each equation. 22x1 = 4
 6.3.68: In 6180, solve each equation. 5x+3 = 15
 6.3.69: In 6180, solve each equation. 3x3= 9x
 6.3.70: In 6180, solve each equation. 4x2= 2x
 6.3.71: In 6180, solve each equation. 8x+14 = 16x
 6.3.72: In 6180, solve each equation. 9x+15 = 27x
 6.3.73: In 6180, solve each equation. 3x27 = 272x
 6.3.74: In 6180, solve each equation. 5x2+8 = 1252x
 6.3.75: In 6180, solve each equation. 4x # 2x2= 162
 6.3.76: In 6180, solve each equation. 92x # 27x2= 31
 6.3.77: In 6180, solve each equation. ex = e3x+8
 6.3.78: In 6180, solve each equation. e3x = e2x
 6.3.79: In 6180, solve each equation. ex2= e3x # 1e2
 6.3.80: In 6180, solve each equation. 1e42x # ex2= e12
 6.3.81: If 4x = 7, what does 42x equal?
 6.3.82: If 2x = 3, what does 4x equal?
 6.3.83: If 3x = 2, what does 32x equal?
 6.3.84: If 5x = 3, what does 53x equal?
 6.3.85: In 8588, determine the exponential function whose graph is given
 6.3.86: In 8588, determine the exponential function whose graph is given
 6.3.87: In 8588, determine the exponential function whose graph is given
 6.3.88: In 8588, determine the exponential function whose graph is given
 6.3.89: Find an exponential function with horizontal asymptote whose graph ...
 6.3.90: Find an exponential function with horizontal asymptote y = 3 whose...
 6.3.91: Suppose that . (a) What is ? What point is on the graph of f ? (b) ...
 6.3.92: Suppose that (a) What is ? What point is on the graph of ? (b) If w...
 6.3.93: Suppose that (a) What is What point is on the graph of g? (b) If wh...
 6.3.94: Suppose that (a) What is What point is on the graph of g? (b) If wh...
 6.3.95: Suppose that (a) What is What point is on the graph of H? (b) If wh...
 6.3.96: Suppose that (a) What is What point is on the graph of F? (b) If wh...
 6.3.97: In 97100, graph each function. Based on the graph, state the domain...
 6.3.98: In 97100, graph each function. Based on the graph, state the domain...
 6.3.99: In 97100, graph each function. Based on the graph, state the domain...
 6.3.100: In 97100, graph each function. Based on the graph, state the domain...
 6.3.101: Optics If a single pane of glass obliterates 3% of the light passin...
 6.3.102: Atmospheric Pressure The atmospheric pressure p on a balloon or pla...
 6.3.103: Depreciation The price p, in dollars, of a Honda Civic DX Sedan tha...
 6.3.104: Healing of Wounds The normal healing of wounds can be modeled by an...
 6.3.105: Drug Medication The function can be used to find the number of mill...
 6.3.106: Spreading of Rumors A model for the number N of people in a college...
 6.3.107: Exponential Probability Between 12:00 PM and 1:00 PM, cars arrive a...
 6.3.108: Exponential Probability Between 5:00 PM and 6:00 PM, cars arrive at...
 6.3.109: Poisson Probability Between 5:00 PM and 6:00 PM, cars arrive at McD...
 6.3.110: Poisson Probability People enter a line for the Demon Roller Coaste...
 6.3.111: Relative Humidity The relative humidity is the ratio (expressed as ...
 6.3.112: Learning Curve Suppose that a student has 500 vocabulary words to l...
 6.3.113: Current in a RL Circuit The equation governing the amount of curren...
 6.3.114: Current in a RC Circuit The equation governing the amount of curren...
 6.3.115: If f is an exponential function of the form with growth factor 3 an...
 6.3.116: Another Formula for e Use a calculator to compute the values of for...
 6.3.117: Another Formula for e Use a calculator to compute the various value...
 6.3.118: Difference Quotient If show that
 6.3.119: If show that
 6.3.120: f1x2 = 1 f1x2 f
 6.3.121: f1ax2 = 3f1x24a f1x2 = a
 6.3.122: 122 and 123 provide definitions for two other transcendental functi...
 6.3.123: 122 and 123 provide definitions for two other transcendental functi...
 6.3.124: Historical de Fermat (16011665) conjectured that the function for w...
 6.3.125: The bacteria in a 4liter container double every minute.After 60 mi...
 6.3.126: Explain in your own words what the number e is. Provide at least tw...
Solutions for Chapter 6.3: Exponential Functions
Full solutions for College Algebra  9th Edition
ISBN: 9780321716811
Solutions for Chapter 6.3: Exponential Functions
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. College Algebra was written by and is associated to the ISBN: 9780321716811. Chapter 6.3: Exponential Functions includes 126 full stepbystep solutions. This textbook survival guide was created for the textbook: College Algebra, edition: 9. Since 126 problems in chapter 6.3: Exponential Functions have been answered, more than 34319 students have viewed full stepbystep solutions from this chapter.

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

Change of basis matrix M.
The old basis vectors v j are combinations L mij Wi of the new basis vectors. The coordinates of CI VI + ... + cnvn = dl wI + ... + dn Wn are related by d = M c. (For n = 2 set VI = mll WI +m21 W2, V2 = m12WI +m22w2.)

Cholesky factorization
A = CTC = (L.J]))(L.J]))T for positive definite A.

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

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.

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.

Inverse matrix AI.
Square matrix with AI A = I and AAl = 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 B1 AI and (AI)T. Cofactor formula (Al)ij = Cji! detA.

Iterative method.
A sequence of steps intended to approach the desired solution.

Jordan form 1 = M 1 AM.
If A has s independent eigenvectors, its "generalized" eigenvector matrix M gives 1 = diag(lt, ... , 1s). The block his Akh +Nk where Nk has 1 's on diagonall. Each block has one eigenvalue Ak and one eigenvector.

lAII = l/lAI and IATI = IAI.
The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n  1, volume of box = I det( A) I.

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A  AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).

Multiplier eij.
The pivot row j is multiplied by eij and subtracted from row i to eliminate the i, j entry: eij = (entry to eliminate) / (jth pivot).

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

Semidefinite matrix A.
(Positive) semidefinite: all x T Ax > 0, all A > 0; A = any RT R.

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.

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

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B II·

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.