NAME : 

 

MATH133 Unit 5 Individual Project – C 

 

Name: 

 

1) Find the domain of the following: 

 

a) xxg5)(.

 

Answer: 

Explain how you obtained your answer here: 

 

b) )4ln()(..xxg

 

Answer: 

 

Show your work or explain how you obtained your answer here: 

 

c) )2log()(..ttg

 

Answer: 

 

Explain how you obtained your answer here: 

 

d) tetf5.5)(.

 

Answer: 

 

Show your work or explain how you obtained your answer here: 

 

 

2) Describe the transformations on the following graph of. 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. 
)log()(xxf.

 


XY-10-9-8-7-6-5-4-3-2-112345678910-10-9-8-7-6-5-4-3-2-1123456789100 


a) )3log()(..xxg

 

Description of transformation: 

Equation(s) for the Vertical Asymptote(s): 

x-intercept in (x, y) form: 

 

 

b) )log()(xxg..

 

Description of transformation: 

Equation(s) for the Vertical Asymptote(s): 

x-intercept in (x, y) form: 

 

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 is the amount of the return. 
P is the principal amount initially deposited. 
ntnrPA..
.
..
.
..1


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 9 years at a rate of 6%. 


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

 
Answer: 

 
Show work in this space. 

 

 

b) Calculate the return (A) if the bank compounds quarterly (n = 4). Round your 
answer to the hundredth's place. 


 Answer: 

 
Show work in this space: 

 

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

 

 Answer: 

 

 Explain: 

 

 

 

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. 
rtPeA.

 
Answer: 

 
Show work in this space: 

 


 

4) Suppose that the function : P=15+40*ln(x) represents the percentage of inbound 
e-mail in the U.S. that is considered spam, where x is the number of years after 2002. 

 


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 2006 to the 
nearest tenth of a percent. 

 

Answer: 

 

Show your work in this space: 

 

 

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

 

Answer: 

 

Show your work in this space: