Math 133 Unit 5 Ip Version A1

NAME : MATH133 Unit 5 Individual Project – A

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. 1)

10 9 8 7 6 5 4 3 2 1 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10

Y

X 1 2 3 4 5 6 7 8 9 10

a)

g(x) = log(x - 5)

Description of transformation: Equation(s) for the Vertical Asymptote(s): x-intercept in (x, y) form: b) g ( x)   log( x)  2

Description of transformation: Equation(s) for the Vertical Asymptote(s): x-intercept in (x, y) form:

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: Show your work in this space: b) What was the average score after 14 months?

Answer:

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c) After what time t was the average score 40%? Answer: Show your work in this space:

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
 r A  P1    n 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. nt 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:

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

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c) If a bank compounds continuously, then the formula used is A  Pe where e is a constant and equals approximately 2.7183. Calculate A with continuous compounding. Round your answer to the nearest cent. rt Answer:

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