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# Mathematics for Business Decisions, Part II Homework 1 for Math 115b, Section: Instructor: Date: by Team:

1. Start with a blank Excel file and use 701 evenly spaced points to plot the graph of over the interval . Recall that Excel uses EXP(x) for . This graph shows you the value of \$2,000 invested at 6%, compounded continuously, for t years. When t is negative, gives the past value. When t is positive, gives the future value of the \$2,000.

2. Use the plot that you made in Question 1 to estimate the length of time that it will take for \$2,000 to grow to \$3,000 at 6%, compounded continuously.

3. Start with a blank Excel file and use 501 evenly spaced points to plot the graph of over the interval . Note that this function is the c.d.f. for an exponential random variable with parameter .

4. Show the graphs of both and in the same plot, over the interval .

5. Use Graphing.xls to plot the graph of over the interval .

6. Use Graphing.xls to plot the graph of over the interval . Note that this function is the p.d.f. for an exponential random variable with parameter .

Mathematics for Business Decisions, Part II Homework 1 for Math 115b, Section: Instructor: Date: by Team: We, the undersigned, maintain that each of us participated fully and equally in the completion of this assignment and that the work contained herein is original. Furthermore, we acknowledge that sanctions will be imposed jointly if any part of this work is found to violate the Student Code of Conduct, the Code of Academic Integrity, or the policies and procedures established for this course. ______________________________ ______________________________ Name (printed) Signature ______________________________ ______________________________ Name (printed) Signature ______________________________ ______________________________ Name (printed) Signature ______________________________ ______________________________ Name (printed) Signature ______________________________ ______________________________ Name (printed) Signature
1. Start with a blank Excel file and use 701 evenly spaced points to plot the graph of over the interval . Recall that Excel uses EXP( x ) for . This graph shows you the value of \$2,000 invested at 6%, compounded continuously, for t years. When t is negative, gives the past value. When t is positive, gives the future value of the \$2,000. Solution: 2. Use the plot that you made in Question 1 to estimate the length of time that it will take for \$2,000 to grow to \$3,000 at 6%, compounded continuously. Solution: 3. Start with a blank Excel file and use 501 evenly spaced points to plot the graph of over the interval . Note that this function is the c.d.f. for an exponential random variable with parameter . Solution: 4. Show the graphs of both and in the same plot, over the interval . Solution: 5. Use Graphing.xls to plot the graph of over the interval . Solution: 6. Use Graphing.xls to plot the graph of over the interval . Note that this function is the p.d.f. for an exponential random variable with parameter . Solution: 7. ( i ) Fit a 3 rd degree polynomial trend line through the data points in the Child Protective Services (Example 1 in the text) example. ( ii ) What caseload does this model predict for the year 2012? Solution:
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