 6.1.1: Explain why the values of an increasing exponential function will e...
 6.1.2: Given a formula for an exponential function, is it possible to dete...
 6.1.3: The Oxford Dictionary defines the word nominal as a value that is s...
 6.1.4: The average annual population increase of a pack of wolves is 25.
 6.1.5: A population of bacteria decreases by a factor of __ 1 8 every 24 h...
 6.1.6: The value of a coin collection has increased by 3.25% annually over...
 6.1.7: For each training session, a personal trainer charges his clients $...
 6.1.8: The height of a projectile at time t is represented by the function...
 6.1.9: Which forests population is growing at a faster rate?
 6.1.10: Which forest had a greater number of trees initially? By how many?
 6.1.11: For the following exercises, consider this scenario: For each year ...
 6.1.12: For the following exercises, consider this scenario: For each year ...
 6.1.13: For the following exercises, consider this scenario: For each year ...
 6.1.14: For the following exercises, determine whether the equation represe...
 6.1.15: For the following exercises, determine whether the equation represe...
 6.1.16: For the following exercises, determine whether the equation represe...
 6.1.17: For the following exercises, determine whether the equation represe...
 6.1.18: For the following exercises, find the formula for an exponential fu...
 6.1.19: For the following exercises, find the formula for an exponential fu...
 6.1.20: For the following exercises, find the formula for an exponential fu...
 6.1.21: For the following exercises, find the formula for an exponential fu...
 6.1.22: For the following exercises, find the formula for an exponential fu...
 6.1.23: For the following exercises, determine whether the table could repr...
 6.1.24: For the following exercises, determine whether the table could repr...
 6.1.25: For the following exercises, determine whether the table could repr...
 6.1.26: For the following exercises, determine whether the table could repr...
 6.1.27: For the following exercises, determine whether the table could repr...
 6.1.28: For the following exercises, use the compound interest formula, A(t...
 6.1.29: For the following exercises, use the compound interest formula, A(t...
 6.1.30: For the following exercises, use the compound interest formula, A(t...
 6.1.31: For the following exercises, use the compound interest formula, A(t...
 6.1.32: For the following exercises, use the compound interest formula, A(t...
 6.1.33: For the following exercises, use the compound interest formula, A(t...
 6.1.34: For the following exercises, use the compound interest formula, A(t...
 6.1.35: For the following exercises, use the compound interest formula, A(t...
 6.1.36: For the following exercises, use the compound interest formula, A(t...
 6.1.37: For the following exercises, use the compound interest formula, A(t...
 6.1.38: For the following exercises, use the compound interest formula, A(t...
 6.1.39: For the following exercises, determine whether the equation represe...
 6.1.40: For the following exercises, determine whether the equation represe...
 6.1.41: For the following exercises, determine whether the equation represe...
 6.1.42: For the following exercises, determine whether the equation represe...
 6.1.43: For the following exercises, determine whether the equation represe...
 6.1.44: For the following exercises, evaluate each function. Round answers ...
 6.1.45: For the following exercises, evaluate each function. Round answers ...
 6.1.46: For the following exercises, evaluate each function. Round answers ...
 6.1.47: For the following exercises, evaluate each function. Round answers ...
 6.1.48: For the following exercises, evaluate each function. Round answers ...
 6.1.49: For the following exercises, evaluate each function. Round answers ...
 6.1.50: For the following exercises, evaluate each function. Round answers ...
 6.1.51: For the following exercises, use a graphing calculator to find the ...
 6.1.52: For the following exercises, use a graphing calculator to find the ...
 6.1.53: For the following exercises, use a graphing calculator to find the ...
 6.1.54: For the following exercises, use a graphing calculator to find the ...
 6.1.55: For the following exercises, use a graphing calculator to find the ...
 6.1.56: The annual percentage yield (APY) of an investment account is a rep...
 6.1.57: Repeat the previous exercise to find the formula for the APY of an ...
 6.1.58: Recall that an exponential function is any equation written in the ...
 6.1.59: In an exponential decay function, the base of the exponent is a val...
 6.1.60: The formula for the amount A in an investment account with a nomina...
 6.1.61: The fox population in a certain region has an annual growth rate of...
 6.1.62: A scientist begins with 100 milligrams of a radioactive substance t...
 6.1.63: In the year 1985, a house was valued at $110,000. By the year 2005,...
 6.1.64: A car was valued at $38,000 in the year 2007. By 2013, the value ha...
 6.1.65: Jamal wants to save $54,000 for a down payment on a home. How much ...
 6.1.66: Kyoko has $10,000 that she wants to invest. Her bank has several in...
 6.1.67: Alyssa opened a retirement account with 7.25% APR in the year 2000....
 6.1.68: An investment account with an annual interest rate of 7% was opened...
Solutions for Chapter 6.1: EXPONENTIAL FUNCTIONS
Full solutions for College Algebra  1st Edition
ISBN: 9781938168383
Solutions for Chapter 6.1: EXPONENTIAL FUNCTIONS
Get Full SolutionsChapter 6.1: EXPONENTIAL FUNCTIONS includes 68 full stepbystep solutions. College Algebra was written by and is associated to the ISBN: 9781938168383. This textbook survival guide was created for the textbook: College Algebra, edition: 1. This expansive textbook survival guide covers the following chapters and their solutions. Since 68 problems in chapter 6.1: EXPONENTIAL FUNCTIONS have been answered, more than 27418 students have viewed full stepbystep solutions from this chapter.

Back substitution.
Upper triangular systems are solved in reverse order Xn to Xl.

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!

CayleyHamilton Theorem.
peA) = det(A  AI) has peA) = zero matrix.

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

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.

Factorization
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to A.

Full column rank r = n.
Independent columns, N(A) = {O}, no free variables.

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].

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.

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.

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).

Partial pivoting.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.

Particular solution x p.
Any solution to Ax = b; often x p has free variables = o.

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

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

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.

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