Finding domain, compound interest and log
Please see the attachment.
1) Find the domain of the following:
a) g(x) = 5^x
b) g(x) = ln(x-4)
c) g(t) = log(t+2)
d) f(t) = 5.5e^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.
a) g(x) = e^x - 5
b) h(x) = -e^x
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.
a) g(x) = log(x-3)
b) g(x) = -log(x)
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 = P (1 + (r/n))^nt
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 $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.
b) Calculate the return (A) if the bank compounds quarterly (n = 4). Round your answer to the hundredth's place.
c) Does compounding annually or quarterly yield more interest? Explain why.
d) If a bank compounds continuously, then the formula used is A = Pe^rt
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 6% interest rate and continuous compounding, what is the answer? Round your answer to the hundredth's place.
5) Suppose that the function P = 11 + 44ln 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.
a) Use this model to approximate the percentage of spam in the year 2006 to the nearest tenth of a percent.
b) Use this model to determine in how many years it will take for the percent of spam to reach 85% provided that law enforcement regarding spammers does not change.© SolutionLibrary Inc. solutionlibary.com 9836dcf9d7 https://solutionlibrary.com/math/algebra/finding-domain-compound-interest-and-log-7dme