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# View of /trunk/NationalProblemLibrary/Rochester/setAlgebra28ExpFunctions/sw6_2_17.pg

Thu Aug 16 23:07:34 2007 UTC (5 years, 9 months ago) by jj
File size: 1448 byte(s)
```Moved problems back into place in the Rochester library, and set up
redirect files from their former locations.
```

```    1 #DESCRIPTION
2 ##  Algebra problem: Natural Exponential Functions
3 ##ENDDESCRIPTION
4
5 ##KEYWORDS('algebra', 'natural exponential function')
6 ## tsch tagged and PAID on 12-12-2003
7
8 ## DBsubject('Algebra')
9 ## DBchapter('Exponential and Logarithmic Functions')
10 ## DBsection('The Natural Exponential Function')
11 ## Date('6/3/2002')
12 ## Author('')
13 ## Institution('')
14 ## TitleText1('College Algebra')
15 ## EditionText1('3')
16 ## AuthorText1('Stewart, Redlin, Watson')
17 ## Section1('6.2')
18 ## Problem1('17')
19
20 DOCUMENT();        # This should be the first executable line in the problem.
21
23 "PG.pl",
24 "PGbasicmacros.pl",
25 "PGchoicemacros.pl",
27 "PGauxiliaryFunctions.pl"
28 );
29
30 TEXT(beginproblem());
32
33 \$p=random(900,1000,5);
34 \$a=random(10,50,5);
35 \$r=\$a/100;
36
37 BEGIN_TEXT
38 The number of bacteria in a culture is given by the function
39 \[
40 n(t)=\$p e^{\$r t}
41 \]
42 where \(t\) is measured in hours.
43 \$BR
44 (a) What is the relative rate of growth of this bacterium population?
45 \$BR
47 \$BR
48 (b) What is the initial population of the culture (at t=0)?
49 \$BR
51 \$BR
52 (c) How many bacteria will the culture contain at time t=5?
53 \$BR
55 \$BR
56 END_TEXT
57
58 \$ans1 = \$a;
59 \$ans2 = \$p;
60 \$ans3 = \$p*exp(\$r*5);
61
62 ANS(num_cmp(\$ans1));
63 ANS(num_cmp(\$ans2));
64 ANS(num_cmp(\$ans3));
65
66 ENDDOCUMENT();        # This should be the last executable line in the problem.
```