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MTH 133 Unit 2 --- A word problem !!!

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John has a choice of using one of two parking garages when he visits downtown:
Option1: $8 an hour for the first two hours, then $2 and hour for each hour more than 2; or
Option 2: $10 for the first hour and $2.50 for each hour more than one.
Let x = total hours parked.
a) Write a mathematical model representing the total parking cost, C, in terms of x for the following (assume John is parking for more than 2 hours):
Option 1: C=8+2(x-2)_________________
Option 2: C=10+2.5(x-1)_________________
b) John plans to spend the day downtown (more than 2 hours), how many total hours would John have to park for the cost of option 1 to be less than option 2. Set up an inequality and show your work algebraically using the information in part a.

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John has a choice of using one of two parking garages when he visits downtown:
Option1: $8 an hour for the first two hours, then $2 and hour for each hour more than 2; or
Option 2: $10 for the ...

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3) 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, "left 1" or "stretched vertically by a factor of 2" are descriptions.

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.
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a) Calculate the return (A) if the bank compounds annually (n = 1). Round your answer to the hundredth's place.
b) Calculate the return (A) if the bank compounds monthly (n = 12). Round your answer to the hundredth's place.
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.
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.

5) Suppose that the function P = 12 + 50ln(x) 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.
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b) Use this model to approximate the year that the percent of spam will reach 90% provided that law enforcement regarding spammers does not change?

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