Math 133 Unit 5 Ip 2

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  • Topic: Asymptote, 1
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Student Answer Form Unit 5 IP_2

April 22, 2011

(1.)

a.

e^(0.05t)=1600
Answer: t=147.556

Show your work:

ln(e^(0.05t))=ln(1600)
0.05t=ln(1600)
(0.05t)/(0.05)=(ln(1600))/(0.05)
t=(ln(1600))/(0.05)
t=20ln(1600)
t=147.556

b.

ln(4x)=3

Answer: x= 5.0214

Show your work:

4x = e^3/4

c.

log2(8-6x) = 5

Answer: x= -4

Show work:
8 – 6x = 2^5
6x = 8 – 32
X = - 24/6

d.

4 + 5e – x = 0

Answer: no solution found

Show work:
e ^ - x = - 4/5

(2.)

a.

g(x) = log (x + 5)

Description of transformation: shifted left 5 units
Equation for vertical asymptote: x = -5
X-intercept in (x, y) form: (- 4, 0)

b.

g(x) = log ( - x)

Description of transformation: no units were moved, stayed in same place Equation for vertical asymptote: x = 0
X-intercept in (x, y) form: (-1, 0)

(3.)

a.

Answer: 68 %

Show work:
S (0) = 68 – 20 * log (0 + 1)
S (0) = 68 – 20 * 0 = 68

b.

Answer:

After 4 months:
54.02%

After 24 months:
40.04%

Show work:
S (4) = 68 – 20 * log (4 + 1) = 54.02

S (24) = 68 – 20 * log (24 + 1) = 40.04

c.

Answer: t = 6.94

Show work:

50 = 68 – 20 log ( t + 1)
t + 1 = 10 ^ (18 / 20) = 7.9433
t= 7.9433 – 1 = 6.94

(4.)

a.

Answer: A= $2,938.66

Show work:

A= 2000 * (1+ 0.08/1) ^ (1*5) = 2938.66

b.

Answer: A= $2,971.89

Show work:

A= 2000 * (1+ 0.08/4) ^ (4*5) = 2791.89

c.

Answer: A= $2,983.66

Show work:

A= 2000 * (2.7183) ^ (0.08 * 5) = 2983.66
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