MATH133 Unit 5 Individual Project – A

1) Describe the transformations on the following graph of f x= log( x) . State the placement of the vertical asymptote and x-intercept after the transformation. For example, vertical shift up 2 or reflected about the x-axis are descriptions.

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-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
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a) g(x) = log(x - 5)

Description of transformation: horizontal shift 5 units to the right

Equation(s) for the Vertical Asymptote(s): x-5=0 x=5

x-intercept in (x, y) form: o=log(x-5) 100=x-5
6=x
6,0

b) gx=- log x+ 2

Description of transformation: Vertical shift 2 units up, reflected about the x axis

Equation(s) for the Vertical Asymptote(s): x=o

x-intercept in (x, y) form:
-logx+2=0
-logx=-2 logx=2 x=102 x=100 (100,0)
2) Students in an English class took a final exam. They took equivalent forms of the exam at monthly intervals thereafter. The average score S(t), in percent, after t months was found to be given by

S(t) = 68 - 20 log (t + 1), t ≥ 0

a) What was the average score when they initially took the test, t = 0?

Answer: s0=68

Show your work in this space: s0=68-20 log (0+1)^0 20 log (0+1)^0 = 0 s0=68

b) What was the average score after 14 months?

Answer: s=44.48 Show your work in this space: s14=68-20log⁡(14+1) s14=68-20log15= s=44.48

c) After what time t was the average score 40%? Answer: t-24.12

Show your work in this space: 40=68-20log(t-1) -28=-20log(t-1) 1.4=log(t-1) T=24.12

3) The formula for calculating the amount of money returned for an initial deposit into a bank account or CD (certificate of deposit) is given by A=P1+YNNT

A  P1  r 
A is the amount of the return.
P is the principal amount initially deposited. r is the annual interest rate (expressed as a decimal). n is the number of compound periods in one year. t is the number of years.

Carry all calculations to six decimals on each intermediate step, then round the final answer to the nearest cent.

Suppose you deposit $3,000 for 6 years at a rate of 7%.

a) Calculate the return (A) if the bank compounds semi-annually. Round your answer to the nearest cent.

Answer: A=$4533.21 Show work in this space. Use ^ to indicate the power or use the Equation
Editor in MS Word. P=3,000 R=7% OR .07 N=2 Semi-annually T=6yrs

A=3,000(.07/2)^2(6) A=$4533.21

b) Calculate the return (A) if the bank compounds monthly. Round your answer to the nearest cent.

Answer: A= $177803.15 Show work in this space: P=3,000 R= .07 N=12 monthly T=6yrs A=3,0001+.071212(6) A=$4533.21

c) If a bank compounds continuously, then the formula used is where e is a A = Pe rt constant and equals approximately 2.7183.

Calculate A with continuous compounding. Round your answer to the nearest cent.

Answer: A=$4565.88

Show work in this space: P=3,000 e=2.7183 R= .07 T=6yrs
A=3000e.076 A=$4565.88