Tutors Answer Your Questions about Exponential-and-logarithmic-functions (FREE)
Question 47674: For a fixed rate, a fixed principal amount, and a fixed compounding cycle, the return is an exponential function of time. Using the formula,A=P(1+r/n)^nt , let r = 8%, P = 1, and n = 1 and give the coordinates (t,A) for the points where t = 0, 1, 2, 3, 4. Round the A value to the tenth's place.
a) Show coordinates in this space.
Show work in this space.
b) Show graph here.
Click here to see answer by Nate(3500)  |
Question 47673: The formula for calculating the amount of money returned for deposit money into a bank account or CD (Certificate of Deposit) is given by the following:
A=P(1+r/n)^nt
A is the amount of returned
P is the principal amount deposited
r is the annual interest rate (expressed as a decimal)
n is the compound period
t is the number of years
Suppose you deposit $20,000 for 3 years at a rate of 8%.
a) Calculate the return (A) if the bank compounds annually (n = 1).
Answer:
Show work in this space. Use ^ to indicate the power.
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) Calculate the return (A) if the bank compounds monthly (n = 12). Round your answer to the hundredth's place.
Answer:
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d) Calculate the return (A) if the bank compounds daily (n = 365). Round your answer to the hundredth's place.
Answer:
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e) What observation can you make about the size of increase in your return as your compounding increases more frequently?
Answer:
f) If a bank compounds continuous, then the formula becomes simpler, that is
where e is a constant and equals approximately 2.7183. Calculate A with continuous compounding. Round your answer to the hundredth's place.
Answer:
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g) Now suppose, instead of knowing t, we know that the bank returned to us $25,000 with the bank compounding continuously. Using logarithms, find how long we left the money in the bank (find t). Round your answer to the hundredth's place.
Answer:
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h) A commonly asked question is, “How long will it take to double my money?” At 8% interest rate and continuous compounding, what is the answer? Round your answer to the hundredth's place.
Answer:
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Click here to see answer by stanbon(57415) |
Question 47953: Use the Laws of Logarithms to rewrite the expression in a form with no logarithm of a product, quotient, or power
log sqrt[x sqrt[y sqrt[z]]]
I got = 1/2 logX [1/2 log y[1/2 log z]]] ?
Thank you so much!
Click here to see answer by stanbon(57415) |
Question 48040: Find the solution of the exponential equation,correct to 4 decimal places:
e^3-5x = 16
I got:
ln(e^3-5x) = ln16
3-5x = ln16
5x = 3-ln16
x= 1/5(3-ln16) = 0.3592
Does this seem correct?
Thank you so much!
Click here to see answer by stanbon(57415) |
Question 48039: Find the solution of the exponential equation,correct to 4 decimal places:
4(1 + 10^5x) = 9
I got:
1 + 10^5x = 9/4
10^5x = 9/4 - 1
10^5x = 3/2
5x = log 3/2 / log10 = 0.1003
x = 0.01938
Thank you so much for all your assistance and guidance!
Click here to see answer by stanbon(57415) |
Question 53609: consider this equation 4x-6y=12
a)what do you suppose the graph of this eqation looks like? justify your answer.
b)solve the equation for y and graph the equation.
c)explain how to find the x- and y-intercept. be complete so that you can give your explanation to someone who is still having trouble with intercepts and he or she will be able to follow and understand your explanation.
d)which form of the equation is the best for finding intercepts quickly?why?
e)use the intercepts you found inpart (c) to graph the line. did you get the same line you got in part (b)? should you? explain
Click here to see answer by checkley71(8403) |
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