You are measuring current flow, measured in amperes for a period measured in min

ID: 3534201 • Letter: Y

Question

You are measuring current flow, measured in amperes for a period measured in minutes. You wish to estimate the total charge carried by the flow over the entire period, expressed in units of ampere*hours. To estimate the charge, you fit a curve C to the current flow measurements. C should be an expression in the variable t (for time). Integrate C with respect to t over the period of time to get the estimate of charge.

To get the curve, use the CurveFitting[Spline] operation of Maple to fit a cubic spline on the following data points:

time in minutes

ampere

1.82

.9239365476E-4

2.65

.1139137110E-2

4.22

.2078590785E-1

5.10

.5920944952E-1

6.75

.2068672027

7.67

.2976709626

9.04

.3253467430

10.5

.1235722307

11.08000000

The data is presented in machine-readable form as a list of x-coordinates, and the matching list of y-coordinates:

xlist := [1.82, 2.65, 4.22, 5.10, 6.75, 7.67, 9.04, 10.5, 11.08000000] ;

ylist := [.9239365476E-4, .1139137110E-2, .2078590785E-1, .5920944952E-1, .2068672027, .2976709626, .3253467430, .1235722307, 0.] ;

(a)What is the value of the spline for the time value of 8.11 minutes? Use the eval command to evaluate the spline at a point. Enter a floating point number.

Part(b):

We want to write a procedure that when given data points and the time value t1=8.11 will compute the result .1038217060E-1 which answer the following question:

What is the total charge, measured in ampere*hours, for the period t=0 to t=8.110000 minutes?

That is, we want to write a procedure of the following form:

splineArea := proc ( xlist, ylist, t1) ..... end proc;

calculates the result given the data points and the length of time.

The procedure should perform three steps: 1.) create a spline, 2) integrate the spline, and 3.) convert the units of the final answer.

We want

splineArea( [1.82, 2.65, 4.22, 5.10, 6.75, 7.67, 9.04, 10.5, 11.08000000], [.9239365476E-4, .1139137110E-2, .2078590785E-1, .5920944952E-1, .2068672027, .2976709626, .3253467430, .1235722307, 0.], 8.11)

to return

.1038217060E-1

We want

splineArea([1.47, 2.04, 3.04, 3.76, 4.73, 5.16, 6.12, 6.380000000], [.5770849034E-1, .1353841986, .3160948781, .4147128301, .4038492492, .3347770092, .7853985362E-1, 0.], 5.38)

to return .1831087200E-1.

Enter the procedure definition for splineArea. Your definition should be of the form
proc(xlist, ylist, t1) .... end proc

While your definition can have more than one line, comments beginning with # should be removed as Maple TA is unable to process those lines in procedures properly.

Your procedure will be tested against the two test cases described above. It will also be tested against a third test case that is similar but not revealed. If your procedure computes a result that agrees with the correct answer in all three cases, it will be marked as correct.

Enter your procedure definition below. Don't forget to leave off the trailing semi-colon after the end proc

splineArea :=