SOLUTION: The volume of a cylinder (think about the volume of a can) is given by V = πr2h where r is the radius of the cylinder and h is the height of the cylinder. Suppose the volume o
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Question 83038: The volume of a cylinder (think about the volume of a can) is given by V = πr2h where r is the radius of the cylinder and h is the height of the cylinder. Suppose the volume of the can is 121 cubic centimeters.
a) Write h as a function of r. Keep "π" in the function's equation.
Answer:
Show work in this space.
b) What is the measurement of the height if the radius of the cylinder is 3 centimeters? Round your answer to the hundredth's place.
Answer:
Show work in this space.
c) Graph this function.
Show graph here.
3) 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
Carry all calculations to 6 decimals on all assignments then round the answer to the
nearest cent.
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:
Show work in this space.
d) Calculate the return (A) if the bank compounds daily (n = 365). Round your answer to the hundredth's place.
Answer:
Show work in this space.
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:
Show work in this space
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:
Show work in this space
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:
Show work in this space.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The volume of a cylinder (think about the volume of a can) is given by V = πr2h where r is the radius of the cylinder and h is the height of the cylinder. Suppose the volume of the can is 121 cubic centimeters.
a) Write h as a function of r. Keep "π" in the function's equation.
Answer:
Show work in this space.
= 121
:
Divide both sides by
h =
:
b) What is the measurement of the height if the radius of the cylinder is 3 centimeters? Round your answer to the hundredth's place.
Answer:
Show work in this space.
h =
h =
h =
h = 4.28 cm
:
c) Graph this function.
Show graph here.
Height (h) is on the vertical axis and radius (r) on the horizontal axis
:
:
3) 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
Carry all calculations to 6 decimals on all assignments then round the answer to the nearest cent.
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:
:
A = 20000(1 + .08/1)^(1*3)
A = 20000(1.08)^3
ln(A) = ln(20000) + ln(1.08^3); using nat logs
ln(A) = ln(20000) + 3*ln(1.08): log equiv of exponents
ln(A) = 9.90349 + 3(.0796)
ln(A) = 9.90349 + .23088
ln(A) = 10.13487; find the anti-log
A = $25,194.22
:
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 .
n=4
A = 20000(1 + .08/4)^(4*3)
A = 20000(1.02)^12
ln(A) = ln(20000) + 12*ln(1.02)
Do it the same way as above
:
c) Calculate the return (A) if the bank compounds monthly (n = 12). Round your answer to the hundredth's place.
Answer:
Show work in this space.
You should be able to do this using the two previous problems as examples
:
d) Calculate the return (A) if the bank compounds daily (n = 365). Round your answer to the hundredth's place.
Answer:
Show work in this space.
A = 20000(1 + .08/365)^365*3
A = 20000(1.000219178^1095)
Same procedure here
:
e) What observation can you make about the size of increase in your return as your compounding increases more frequently?
Answer: notice that after a certain point, increasing the compounding periods does not make a large difference in the return amt
:
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:
Show work in this space
These can be easily done on a good calculator
A = P(e^rt)
A = 20000(e^(.08*3)); enter this into the calc
A = 25424.98;
:
:
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:
Show work in this space
P(e^rt) = A
A = 25000; r=.08; find t:
20000(e^.08t) = 25000
e^.08t = 25000/20000; divided both sides by 20000
e^.08t = 1.25
ln(e^.08t) = ln(1.25)
.08t = .22314355: remember the ln of e, is 1
t = .22314355/.08
t = 2.79 years
:
Check on a calculator: 20000*e^(2.79*.08) = 25,001
:
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:
Show work in this space.
Let A = 2 and P = 1
1(e^.08t) = 2
.08t*ln(e) - ln(2)
.08t = .693147
t = .693147/.08
t = 8.66 yrs to double your money
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