Math 133 Unit 5 Essay
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
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