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| 1 : | jj | 61 | ## DESCRIPTION |
| 2 : | jjholt | 459 | ## Instantaneous Rate of Change |
| 3 : | jj | 61 | ## ENDDESCRIPTION |
| 4 : | |||
| 5 : | jjholt | 459 | ## KEYWORDS('instantaneous', 'rate of change', 'application', 'derivative') |
| 6 : | jj | 61 | ## Tagged by YL |
| 7 : | |||
| 8 : | ## DBsubject('Calculus') | ||
| 9 : | jjholt | 459 | ## DBchapter('Differentiation') |
| 10 : | ## DBsection('Rates of Change in the Natural and Social Sciences') | ||
| 11 : | jj | 61 | ## Date('') |
| 12 : | ## Author('') | ||
| 13 : | ## Institution('ASU') | ||
| 14 : | jjholt | 480 | ## TitleText1('Calculus: Early Transcendentals') |
| 15 : | ## EditionText1('5') | ||
| 16 : | jj | 61 | ## AuthorText1('Stewart') |
| 17 : | jjholt | 459 | ## Section1('3.3') |
| 18 : | jj | 61 | ## Problem1('') |
| 19 : | |||
| 20 : | jjholt | 481 | ## TitleText2('Calculus: Early Transcendentals') |
| 21 : | ## EditionText2('6') | ||
| 22 : | ## AuthorText2('Stewart') | ||
| 23 : | ## Section2('3.7') | ||
| 24 : | ## Problem2('') | ||
| 25 : | |||
| 26 : | jj | 61 | DOCUMENT(); |
| 27 : | |||
| 28 : | loadMacros( | ||
| 29 : | "PG.pl", | ||
| 30 : | "PGbasicmacros.pl", | ||
| 31 : | "PGchoicemacros.pl", | ||
| 32 : | "PGanswermacros.pl", | ||
| 33 : | "PGauxiliaryFunctions.pl" | ||
| 34 : | ); | ||
| 35 : | |||
| 36 : | gage | 268 | TEXT(beginproblem()); |
| 37 : | jj | 61 | $showpartialcorrectanswers = 1; |
| 38 : | |||
| 39 : | $a = random(.3,.9, .1); | ||
| 40 : | $b = random(1,5,1); | ||
| 41 : | $c = random(7,12,1); | ||
| 42 : | |||
| 43 : | TEXT(EV2(<<EOT)); | ||
| 44 : | A coal-burning electrical generating plant emits sulfur dioxide | ||
| 45 : | into the surrounding air. The concentration \(C(x)\), in parts per | ||
| 46 : | million, is approximately given by the function | ||
| 47 : | \[ C(x) = \frac{$a}{x^2}, \] | ||
| 48 : | where \(x\) is the distance away from the plant in miles. | ||
| 49 : | $BR | ||
| 50 : | The instantaneous rate of change of the sulfur dioxide | ||
| 51 : | concentration: | ||
| 52 : | $BR | ||
| 53 : | (A) $b miles from the plant = \{ans_rule(30) \} | ||
| 54 : | $BR | ||
| 55 : | EOT | ||
| 56 : | |||
| 57 : | $ans = (-2)*$a*(($b)**(-3)); | ||
| 58 : | gage | 268 | ANS(num_cmp($ans)); |
| 59 : | jj | 61 | |
| 60 : | TEXT(EV2(<<EOT)); | ||
| 61 : | (B) $c miles from the plant = \{ans_rule(30) \} | ||
| 62 : | $BR | ||
| 63 : | EOT | ||
| 64 : | |||
| 65 : | $ans = -2*$a*($c**(-3)); | ||
| 66 : | gage | 268 | ANS(num_cmp($ans)); |
| 67 : | jj | 61 | |
| 68 : | |||
| 69 : | ENDDOCUMENT(); |
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