 9.4.1: Practice using the exponential growth formula by completing the tab...
 9.4.2: Practice using the exponential growth formula by completing the tab...
 9.4.3: Practice using the exponential growth formula by completing the tab...
 9.4.4: Practice using the exponential growth formula by completing the tab...
 9.4.5: Practice using the exponential growth formula by completing the tab...
 9.4.6: Practice using the exponential growth formula by completing the tab...
 9.4.7: Practice using the exponential decay formula by completing the tabl...
 9.4.8: Practice using the exponential decay formula by completing the tabl...
 9.4.9: Practice using the exponential decay formula by completing the tabl...
 9.4.10: Practice using the exponential decay formula by completing the tabl...
 9.4.11: Practice using the exponential decay formula by completing the tabl...
 9.4.12: Practice using the exponential decay formula by completing the tabl...
 9.4.13: Solve. Unless noted otherwise, round answers to the nearest whole. ...
 9.4.14: Solve. Unless noted otherwise, round answers to the nearest whole. ...
 9.4.15: Solve. Unless noted otherwise, round answers to the nearest whole. ...
 9.4.16: Solve. Unless noted otherwise, round answers to the nearest whole. ...
 9.4.17: Solve. Unless noted otherwise, round answers to the nearest whole. ...
 9.4.18: Solve. Unless noted otherwise, round answers to the nearest whole. ...
 9.4.19: Solve. Unless noted otherwise, round answers to the nearest whole. ...
 9.4.20: Solve. Unless noted otherwise, round answers to the nearest whole. ...
 9.4.21: Practice using the exponential decay formula with halflives by com...
 9.4.22: Practice using the exponential decay formula with halflives by com...
 9.4.23: Practice using the exponential decay formula with halflives by com...
 9.4.24: Practice using the exponential decay formula with halflives by com...
 9.4.25: Solve. Round answers to the nearest tenth.A form of nickel has a ha...
 9.4.26: Solve. Round answers to the nearest tenth.A form of uranium has a h...
 9.4.27: By inspection, find the value for x that makes each statement true....
 9.4.28: By inspection, find the value for x that makes each statement true....
 9.4.29: By inspection, find the value for x that makes each statement true....
 9.4.30: By inspection, find the value for x that makes each statement true....
 9.4.31: An item is on sale for 40% off its original price. If it is then ma...
 9.4.32: Uranium U232 has a halflife of 72 years. What eventually happens ...
Solutions for Chapter 9.4: Exponential Growth and Decay Functions
Full solutions for Intermediate Algebra  6th Edition
ISBN: 9780321785046
Solutions for Chapter 9.4: Exponential Growth and Decay Functions
Get Full SolutionsIntermediate Algebra was written by and is associated to the ISBN: 9780321785046. Chapter 9.4: Exponential Growth and Decay Functions includes 32 full stepbystep solutions. Since 32 problems in chapter 9.4: Exponential Growth and Decay Functions have been answered, more than 59952 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Intermediate Algebra, edition: 6. This expansive textbook survival guide covers the following chapters and their solutions.

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

Circulant matrix C.
Constant diagonals wrap around as in cyclic shift S. Every circulant is Col + CIS + ... + Cn_lSn  l . Cx = convolution c * x. Eigenvectors in F.

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

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

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

Determinant IAI = det(A).
Defined by det I = 1, sign reversal for row exchange, and linearity in each row. Then IAI = 0 when A is singular. Also IABI = IAIIBI and

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

Ellipse (or ellipsoid) x T Ax = 1.
A must be positive definite; the axes of the ellipse are eigenvectors of A, with lengths 1/.JI. (For IIx II = 1 the vectors y = Ax lie on the ellipse IIA1 yll2 = Y T(AAT)1 Y = 1 displayed by eigshow; axis lengths ad

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.

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

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

Normal equation AT Ax = ATb.
Gives the least squares solution to Ax = b if A has full rank n (independent columns). The equation says that (columns of A)ยท(b  Ax) = o.

Polar decomposition A = Q H.
Orthogonal Q times positive (semi)definite H.

Projection p = a(aTblaTa) onto the line through a.
P = aaT laTa has rank l.

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).

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

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).