Algebra II Chapter 5 Review SOLUTIONS

Solutions are listed below with work provided for some questions. Answers for different parts of one question are separated by semicolons - i.e. for 1) a, b, c the solutions would be written 1) solution to a; solution to b; solution to c. So, without further ado:

Solutions
1) 0.82^6 = 0.3
2) 5*4^2.4 = 139.3
3) for t = 0, y = 4^7; for t = 3/2 = 1.5, y = 4^7 * 4^1.5 = 4^8.5 = 131,072
4) y = 50(2)^x (exponential function with starting value 50 and a growth rate of 2)
5) (xz/w^5) + (x^2/w^3)
6) x = -4
7) x = 4; x = 2
8) 2
9) 4
10) 12x^6
11) Use the points to write two equations in point-ratio form, then solve for b to get y = 0.277(3)^(x+1) or y = 0.031(3)^(x+3)
12) y = 6(2)^x
13) put 70 in for p to get s =45.68; put 50 in for s to get p = 120.43
14) y = 4800(2)^t; y = 4800(2)^4 = 76,800
15) y = 6x + 9
16) y = (x^2 + 6x + 1)/(-8)
17) y = (x - 2)/3; yes - there is only one output for each input
18) The graphs should be reflections about the line y = x. The inverse function should be y = (x + 2)/3
19) Find the inverse function, then put 6 in for x. You should get -2. Put -2 in the original function for x. The end result should be what you started with: 6. This is because composing a function with its inverse will undo itself.
20) -8
21) 8
22) x = 1.97 (remember that 4.7 should be the base and 21 should be a)
23) 4
24) -7
25) 3.17
26) To begin, take the log of both sides then use the power property of logarithms to bring the exponent down. You should get x = 5.03
27) 2.2694 (d)
28) Use your logarithm properties to simplify! Remember that taking the antilog of something leaves you with what you started with - i.e. if I had log x, then 10^log x = x. If I had log 2, 10^log 2 = 2, and so on. So if I had log (x-6)/(x-1), 10^log (x-6)/(x-1) = (x-6)/(x-1) and if I do it to one side, I have to do it to the other, too! x = 36
29) True - this is the quotient property of logarithms
30) log (base p) 4. You should use the power property and quotient property to simplify.
31) 3rd root of m squared; 4logb; logx / log7; y/x^2; 2^(3x + 3y); log10/3
32) 4.19; 0.001; 0.4; -8.46; 2.40, -2.40; 6
33) Write an exponential equation with a = 23000, b = 1 - 0.17. Set it equal to 10000, then solve for x. x = 4.47 years (about 4 years, 6 months)
34) ((x + 1)/2)^2 - 3; 13/4; 6
35) a = 7.44, b = 22.89; 0.47; $48.94; 2.14 hours (2 hours, 8 minutes)
36) y = ((x-3)/5)^2 + 2; 51/25; 5

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