- 9.6.1: Police use blood alcohol content (BAC) to measure the percent conce...
- 9.6.2: Is the formula for power output an example of exponential growth or...
- 9.6.3: Find the power available after 100 days.
- 9.6.4: Ten watts of power are required to operate the equipment in the sat...
- 9.6.5: The weight of a bar of soap decreases by 2.5% each time it is used....
- 9.6.6: Write an exponential growth equation of the form y = a e kt for Fay...
- 9.6.7: Use your equation to predict the population of Fayette County in 2015.
- 9.6.8: Zeus Industries bought a computer for $2500. If it depreciates at a...
- 9.6.9: A certain medication is eliminated from the bloodstream at a steady...
- 9.6.10: A paleontologist finds a bone of a human. In the laboratory, she fi...
- 9.6.11: An anthropologist studying the bones of a prehistoric person finds ...
- 9.6.12: The Martins bought a condominium for $145,000. Assuming that the va...
- 9.6.13: Assuming this rate of growth continues, what will the GDP of the Un...
- 9.6.14: In what year will the GDP reach $20 trillion?
- 9.6.15: Find the constant k for this type of bacteria under ideal conditions
- 9.6.16: Write the equation for modeling the exponential growth of this bact...
- 9.6.17: In 1928, when the high jump was first introduced as a womens sport ...
- 9.6.18: The Mendes family bought a new house 10 years ago for $120,000. The...
- 9.6.19: Write an equation in the form t = a n b , where t is the time in mi...
- 9.6.20: According to the formula, how long should you cook six 8-ounce pota...
- 9.6.21: Explain how to solve y = (1 + r ) t for t
- 9.6.22: Give an example of a quantity that grows or decays at a fixed rate....
- 9.6.23: The half-life of radium is 1620 years. When will a 20-gram sample o...
- 9.6.24: Use the information about car values on page 544 to explain how you...
- 9.6.25: The curve represents a portion of the graph of which function? Y / ...
- 9.6.26: The curve represents a portion of the graph of which function? Y / ...
- 9.6.27: Write an equivalent exponential or logarithmic equation.
- 9.6.28: Write an equivalent exponential or logarithmic equation.
- 9.6.29: Write an equivalent exponential or logarithmic equation.
- 9.6.30: Solve each equation or inequality. Round to four decimal places.
- 9.6.31: Solve each equation or inequality. Round to four decimal places.
- 9.6.32: Solve each equation or inequality. Round to four decimal places.
- 9.6.33: Write an expression to represent the share of the profits each nons...
- 9.6.34: Simplify this expression.
- 9.6.35: Write an expression in simplest form to represent the share of the ...
- 9.6.36: Write the number of pounds of pecans forecasted by U.S. growers in ...
- 9.6.37: Write the number of pounds of pecans produced by Georgia in 2003 in...
- 9.6.38: What percent of the overall pecan production for 2003 can be attrib...
Solutions for Chapter 9.6: Exponential Growth and Decay
Full solutions for California Algebra 2: Concepts, Skills, and Problem Solving | 1st Edition
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.
Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).
Column space C (A) =
space of all combinations of the columns of A.
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.
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
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.
Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.
Invert A by row operations on [A I] to reach [I A-I].
Identity matrix I (or In).
Diagonal entries = 1, off-diagonal entries = 0.
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.
Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).
Krylov subspace Kj(A, b).
The subspace spanned by b, Ab, ... , Aj-Ib. 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.
lA-II = 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.
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).
Row space C (AT) = all combinations of rows of A.
Column vectors by convention.
Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).
Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.
Symmetric matrix A.
The transpose is AT = A, and aU = a ji. A-I is also symmetric.
Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and A-I are BT AT and (AT)-I.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.