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.
______________________________
Name (printed)
______________________________
Signature
______________________________
Name (printed)
______________________________
Signature
______________________________
Name (printed)
______________________________
Signature
______________________________
Name (printed)
______________________________
Signature
(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 f (t )  2,000  e 0.06 t over the
interval [12,12] . Recall that Excel uses EXP(x) for e x . This graph shows you the value of $2,000 invested at 6%,
compounded continuously, for t years. When t is negative, f (t ) gives the past value. When t is positive, f (t ) gives the
future value of the $2,000.
Problem 2 Plot the graph of f ( x)  0.00002  x 2  100 over the interval [0,2000].
Problem 3
Start with a blank Excel file and use 501 evenly spaced points to plot the graph of f ( x) 
1
2π
2
 e 0.5x over the
interval [4,4] . 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 f ( x )  g ( x) .
( 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 f ( x)  x and g ( x)  0.25 x  1 in the same plot, over the interval [0,8] . 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
f ( x)  g ( x) . (iii) How would you describe the relationship between the graphs of f and g at the point where they
intersect?
Problem 6
0
 x /
1  e
The c.d.f. for an exponential random variable, X, with parameter  is given by F ( x)  
the three graphs of F, with   2, 3, and 4 , in a single plot, over the interval [5,15] .
if x  0
. Show
if 0  x
Problem 7
x0

0
Use Graphing.xls to plot the graph of f ( x)   1
e

 2.5
exponential random variable with parameter   2.5 .
 x / 2.5
0 x
. Note that this function is the p.d.f. for an
Problem 8
Use Graphing.xls to plot the graph of f ( x) 
1
2π
2
 e 0.5x over the interval [5,5] . To enter the constant  in
Excel, type PI(). In Excel, the square root function is entered as SQRT