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Precalculus Essay

547 words - 3 pages

Section 4.2
8. Given: F(x) = 3x and G(x) = (1/4)x, what is G(-3)? G(-3) = (1/4)-3 = 64

14. Graph F(x) = 4x
X F(x)
0 1
1 4
2 16
-1 .25

58. 32t+1=161-t
(43)t+1=(42)1-t
4(3t+3)=4(2-2t)
3t+3 = 2-2t
5t = -1
T = -1/5

66. 1/81 = K-4
3-4=K-4
K=3
74. A= \$45,000(1 + .035/12)12
\$46,600.51

Section 4.3
4. 25=32 therefore log232=5

14. X=log3(1/81), therefore 3x=1/81
X=-4

16. logx(27/64) = 3
X3= 27/64
X = (27/64)
X=3/4

46. F(x) = log10X
X Y = log10X
1 0
2 .301
3 .477
4 .602
5 .699

62. log2 2 /5
Log22 + log2 -log25
1+log231/2-log25
...view middle of the document...

59, function is very accurate
b. As the percentage increases towards 100% the rate of kids that volunteer will slow and a large number of years will be needed to continue to approach 100% representative of a logarithmic function. An exponential function would reach 100% in a few years, which is not representative of the rate at which the kids are volunteering.
56.
H=-[.521log2.521+.324log2.324+.0811log2.0811+.074log2.074]
H=1.59
Section 4.5
6. 5x=13
Ln5x=13
Xln5=ln13
X = ln13/ln5 = 1.59

24. 5(1.2)3x-2 + 1 = 7
5(1.2)3x-2=6
ln1.23x-2=ln6/5
(3x-2)ln1.2 = ln6/5
3x-2 = ln(6/5)/ln1.2
3x = [ln(6/5)/ln1.2] +2
X = [[ln(6/5)/ln1.2] +2]/3
X=1

60. R=p-kln(t)
r-p=-kln(t)
p-r=kln(t)
(p-r)/k = ln(t)
e[(p-r)/k]=t

76. 20,000=16,000(1+r/4)5.25*4
1.25=(1+r/4)21
Ln1.25 = 21ln(1+r/4)
Ln1.25/21 =ln(1+r/4)
e.010626=1+r/4
1.0107 = 1+r/4
.0107=r/4
r=.04, therefore rate =40%

94. (ex)2-4ex+3 = (ex-3)(ex-1)

Section 4.6
2. Given: y=2e.2x
A. 3 mil = 2e.2x
1.5mil = e.2x
Ln1.5 = .2x
X=ln1.5/.2 = 2.03 years
B. 2e.2x=6
e.2x=3
lne.2x=ln3
.2x=ln3
X=ln3/.2=5.49

10. M=1 M=3
1=6-5/2logx 3=6-5/2logx
5=5/2logx 3=5/2logx
10=5logx 6=5logx
2=logx 6/5=logx
X=100 X=15.8
Ratio; 100:16 or 25:4

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