GP Unit 4

Instructions:

• Identify the document by typing your full name and section number next to the yellow text.
• Rename the file by adding your last names to current file name (e.g., "u4gp_lastnames.doc").
• Type your answers next to the yellow text.
  • Answers requiring decimal places should be rounded to two decimals. This includes rounding dollar and cent amounts to the nearest cent.
• To show your work, you will need to include

• the formula with substituted values.
• the final calculated answer with units.

• To utilize the scientific calculator on your computer, do the following:
  • Open the calculator (if it is not in the accessories folder, then select Run from the Start menu)
  • Select View from the drop down menu
  • Select Scientific to utilize the calculator.
  • Note that x^y computes any number to any power (integer, fraction, decimal).

Please add your file.

1. An open-top box is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out.
   1. Find the function V that represents the volume of the box in terms of x .
      
      Answer
      
      
      
      
   2. Graph this function.
      Show Graph here
      
      
      
      
   3. Using the graph, what is the value of x that will produce the maximum volume?
      Answer
      
      
      
2. The volume of a cylinder (think about the volume of a can) is given by V = π 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.
   1. Write h as a function of r .
      Answer
   2. What is the measurement of the height if the radius of the cylinder is 2 centimeters?
      Answer
      
      Show work in this space.
      
      
   3. Graph this function.
      Show graph here
      
      
      
      
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
   \[A=P{{\left( 1+\frac{r}{n} \right)}^{nt}}\]
   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.
   
   Suppose you deposit $10,000 for 2 years at a rate of 10%.
   1. Calculate the return ( A ) if the bank compounds annually ( n = 1).
      Answer:
      Show work in this space. Use ^ to indicate the power.
      
      
      
   2. Calculate the return ( A ) if the bank compounds quarterly ( n = 4).
      Answer:
      Show work in this space.
      
      
   3. Calculate the return ( A ) if the bank compounds monthly ( n = 12).
      Answer:
      
      Show work in this space
      
      
      
      
   4. Calculate the return ( A ) if the bank compounds daily ( n = 365).
      Answer:
      
      Show work in this space
      
      
      
   5. What observation can you make about the increase in your return as your compounding increases more frequently?
      Answer:
      
      
      
      
   6. If a bank compounds continuous, then the formula takes a simpler form, that is
      \[A=P{{e}^{rt}}\]
      where e is a constant and equals approximately 2.7183.
      Calculate A with continuous compounding.
      Answer:
      
      Show work in this space.
      
      
      
   7. Now suppose, instead of knowing t , we know that the bank returned to us $15,000 with the bank compounding continuously. Using logarithms, find how long we left the money in the bank (find t ).
      Answer:
      Show work in this space
      
      
   8. A commonly asked question is, "How long will it take to double my money?" At 10% interest rate and continuous compounding, what is the answer?
      Answer:
      
      Show work in this space
      
      
4. For a fixed rate, a fixed principal amount, and a fixed compounding cycle, the return is an exponential function of time. Using the formula, \[A=P{{\left( 1+\frac{r}{n} \right)}^{nt}}\] , let r = 10%, P = 1, and n = 1 and give the coordinates ( t , A ) for the points where t = 0, 1, 2, 3, 4.
   1. Show coordinates in this space
      Show work in this space
      Show graph here
      
      
      
      
      
5. Logarithms:
   1. Using a calculator, find log 10000 where log means log to the base of 10.
      Answer:
      
      
      
      
   2. Most calculators have 2 different logs on them: log, which is based 10, and ln, which is based e . In computer science, digital computers are based on the binary numbering system which means that there are only 2 numbers available to the computer, 0 and 1. When a computer scientist needs a logarithm, he/she needs a log to base 2 which is not on any calculator. To find the log of a number to any base, we can use a conversion formula as shown here:
      \[{{\log }_{b}}a=\frac{\log a}{\log b}\]
      Using this formula, find \[{{\log }_{2}}10000\] .
      Answer:

Show work in this space

Price: $16.02

Solution: The downloadable solution consists of 7 pages, 902 words and 3 charts.
Deliverable: Word Document