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1 ## DESCRIPTION
2 ## Calculus
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('exponential growth' 'population')
6 ## Tagged by tda2d
7
8 ## DBsubject('Calculus')
9 ## DBchapter('Differential Equations')
10 ## DBsection('Exponential Growth and Decay')
11 ## Date('')
12 ## Author('')
13 ## Institution('Dartmouth')
14 ## TitleText1('Calculus')
15 ## EditionText1('5')
16 ## AuthorText1('Stewart')
17 ## Section1('10.4')
18 ## Problem1('')
19
20
21 DOCUMENT();
23            "PGbasicmacros.pl",
24            "PGchoicemacros.pl",
26            "PGauxiliaryFunctions.pl",
27            "PGgraphmacros.pl",
28            "Dartmouthmacros.pl");
29
30
31 ## Do NOT show partial correct answers
33
34 \$initial= random(300,900,100);
35 \$later = random(3000,10000,1000);
36 \$t1 = random(3,9);
37
38
39 ## Ok, we are ready to begin the problem...
40 ##
41 TEXT(beginproblem());
42
43
44 BEGIN_TEXT
45 \$BR
46
47 A bacteria culture starts with \$initial bacteria and grows at a rate
48 proportional to its size.  After \$t1 hours, there are \$later bacteria.
49 \$PAR
50
51 \$BBOLD A. \$EBOLD
52 Find an expression for the number of bacteria after \(t\) hours.\$BR
53 \{ans_rule(60)\}
54 \$PAR
55
56 \$BBOLD B. \$EBOLD
57 Find the number of bacteria after \{\$t1 + 1\} hours.\$BR
58 \{ans_rule(30)\}
59 \$PAR
60
61 \$BBOLD C. \$EBOLD
62 Find the growth rate after \{\$t1 + 1\} hours.\$BR
63 \{ans_rule(30)\}
64 \$PAR
65
66 \$BBOLD D. \$EBOLD
67 After how many hours will the population reach 30000?\$BR
68 \{ans_rule(30)\}
69 \$PAR
70
71 \$PAR
72 END_TEXT
73 \$k = log(\$later/\$initial)/\$t1;
74 ANS(fun_cmp("\$initial*exp(\$k*t)", var=>['t']));
75 ANS(num_cmp(\$initial*exp(\$k*(\$t1+1)), tol=>2));
76 ANS(num_cmp(\$initial*exp(\$k*(\$t1+1))*\$k, tol=>2));
77 ANS(num_cmp(log(30000/\$initial)/\$k, tol=>2));
78
79 ENDDOCUMENT();
80
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