# various problem in GP Unit 4

1) An open-top box is to be constructed from a 6 foot by 8 foot rectangular cardboard by cutting out equal squares at each corner and folding up the flaps. Let x denote the length of each side of the square to be cut out.

a) Find the function V that represents the volume of the box in terms of x.

b) Graph this function and show the graph over the valid range of the variable x..

c) Using the graph, what is the value of x that will produce the maximum volume?

2) The volume of a cylinder (think about the volume of a can) is given by V = pi*r^2*h where r is the radius of the cylinder and h is the height of the cylinder. Suppose the volume of the can is 100 cubic centimeters.

a) Write h as a function of r. Keep "pi" in the function's equation.

b) What is the measurement of the height if the radius of the cylinder is 2 centimeters? Round your answer to the nearest whole number.

c) Graph this function.

3) The formula for calculating the amount of money returned for an initial deposit money into a bank account or CD (Certificate of Deposit) is given by:

A is the amount of returned.

P is the principal amount initially 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 $10,000 for 2 years at a rate of 10%.

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) Calculate the return (A) if the bank compounds monthly (n = 12). Round your answer to the hundredth's place.

d) Calculate the return (A) if the bank compounds daily (n = 365). Round your answer to the hundredth's place.

e) What observation can you make about the size of the increase in your return as your compounding increases more frequently?

f) If a bank compounds continuously, then the formula takes a 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.

#### Solution Preview

Please see the attached file for detailed solution and graphs.

1) The bottom of the box is a rectangular. The length of the ...

#### Solution Summary

The solution is comprised of detailed step-by-step solutions in group project unit 4. The solution explains the calculation of money returned for different compounding periods. It also shows detailed explainations of finding the function of the volume of an open-top box, which is constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps.