Business Mathematics II

Homework 1

for

Math 115b, Sections:

Instructor: Ratnayaka

Due Date:

by

Team:

We, the undersigned, affirm 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.

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(You must provide a printout of the excel formulas used, graphs, sample data & workings for the problems)

Problem 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.

Problem 2 Plot the graph of over the interval

Problem 3

Start with a blank Excel file and use 501 evenly spaced points to plot the graph of over the interval . To enter the constant in Excel, type PI(). In Excel, the square root function is entered as SQRT.

Problem 4

Use the plot of f and g from Example 2 to estimate the two values of x for which .

( Example 2 is in MBD 2 Proj1.ppt(course file )-slide #12 & look at the graph in the sheet Graph 2 of course file Graph Examples.xls (course file ) )

Problem 5

(i) Show the graphs of both and in the same plot, over the interval . Recall that in Excel, the square root function is entered as SQRT. (ii) Use your plot to estimate the coordinates of the point at which . (iii) How would you describe the relationship between the graphs of f and g at the point where they intersect?

Problem 6

The c.d.f. for an exponential random variable, X, with parameter is given by . Show the three graphs of F, with , in a single plot, over the interval .

Problem 7

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

Problem 8

Use Graphing.xls to plot the graph of over the interval . To enter the constant in Excel, type PI(). In Excel, the square root function is entered as SQRT