This is a Mathematica file to solve Problem 68, p. 309.

Note the funny way that functions are defined: using the underscore.

[Graphics:Images/5.3_gr_1.gif]
[Graphics:Images/5.3_gr_2.gif]
[Graphics:Images/5.3_gr_3.gif]
[Graphics:Images/5.3_gr_4.gif]
[Graphics:Images/5.3_gr_5.gif]

[Graphics:Images/5.3_gr_6.gif]

[Graphics:Images/5.3_gr_7.gif]
[Graphics:Images/5.3_gr_8.gif]
[Graphics:Images/5.3_gr_9.gif]

But since -2 is less than zero, it's not in the domain (time must be positive). Only 2 hours is an interesting potential critical point.

[Graphics:Images/5.3_gr_10.gif]
[Graphics:Images/5.3_gr_11.gif]

This is less than zero, so we have a relative max. That's good!

[Graphics:Images/5.3_gr_12.gif]
[Graphics:Images/5.3_gr_13.gif]

So 3/4% is the maximum concentration.

[Graphics:Images/5.3_gr_14.gif]

[Graphics:Images/5.3_gr_15.gif]

[Graphics:Images/5.3_gr_16.gif]

Yep! Sure enough, a maximum.


Converted by Mathematica      November 16, 2004