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# Several algebra problems explained in this solution

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1) Find the domain of the following:

a)

b)

c)

d)

2) Describe the transformations on the following graph of . State the placement of the horizontal asymptote and y-intercept after the transformation. For example, "left 1" or "reflected about the y-axis" are descriptions.

a)

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

b)

Description of transformation:

Equation(s) for the Horizontal Asymptote(s):
y-intercept in (x, y) form:

3) Describe the transformations on the following graph of . State the placement of the vertical asymptote and x-intercept after the transformation. For example, "left 1" or "stretched vertically by a factor of 2" are descriptions.

a)

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

b)

Description of transformation:

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

4) 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 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 \$4,000 for 8 years at a rate of 7%.

a) Calculate the return (A) if the bank compounds annually (n = 1). Round your answer to the hundredth's place.

Show work in this space. Use ^ to indicate the power or use the Equation Editor in MS Word.

b) Calculate the return (A) if the bank compounds monthly (n = 12). Round your answer to the hundredth's place.

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c) Does compounding annually or monthly yield more interest? Explain why.

d) If a bank compounds continuously, then the formula used is
where e is a constant and equals approximately 2.7183.
Calculate A with continuous compounding. Round your answer to the hundredth's place.

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e) A commonly asked question is, "How long will it take to double my money?" At 7% interest rate and continuous compounding, what is the answer? Round your answer to the hundredth's place.

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5) Suppose that the function represents the percentage of inbound e-mail in the U.S. that is considered spam, where x is the number of years after 2001.

Carry all calculations to six decimals on each intermediate step, when necessary.

a) Use this model to determine the percentage of spam in the year 2005. Round your answer to two decimal places.

Show your work in this space:

b) Use this model to determine how many years it will take (to two decimal places) for the percent of spam to reach 90% provided that law enforcement regarding spammers does not change?