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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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## MTH133: Unit 5 Individual Project - B

Please see attached file for full problem description.

Exponential and Logarithmic Functions: MTH133: Unit 5 Individual Project - B

See attached file for full problem description.

1) Find the domain of the following:
a) f(t) = log(t -5)
b) g(x) = 5 *e^x
c) g(x) = ln(t + 4)
d) g(t) = 5^t

2) Describe the transformations on the following graph of f(x) = e^x. State the placement of the horizontal asymptote and y-intercept after the transformation. For example, "left 1" or "rotated about the y-axis" are descriptions.

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.
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.
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.
a) Use this model to approximate the percentage of spam in the year 2005.
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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