4.4 Applications - MA 160 Section 4.4 Worksheet Continued...

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Unformatted text preview: MA 160 Section 4.4 Worksheet Continued with Appiications Name Go v\ G» a: +9 .. Properties of Definite Integral (Area and Average Value) 1. A company determines that its marginal revenue per day is R'(t) = 208‘ — 3t, R(O) = 0 where tilt) is the total accumulated revenue, in dollars, on the tth day. The company’s marginal cost per day is C'(t) = 20 e 21‘, C(O) = 0, where C(t) is the total accumulated cost , in dollars, on the 1“ th day. a. Whatisthemarginalprofitfunction? e 1,— PJCE} = R'Yt-l - (1"(6) 2: 906?. - Sf-(cilo-Oclfl: «5th -— 3f—10+;1t F‘ée) ~— ao ENE—t "9.0 b. Find the total profit forthe first 10 days. . "a f - t 2‘:3 m to ‘- 100906 —f-Aa)d{:aoe ""r “—104: :20: w to 7—206 _ 50‘ Aoowao = oZ’Oe' -—.;t’?'o :-_ 3-990 2.59 3.1 c. Find the average daily profit for the first 10 days. '10 _ ..- HQ- ‘ w. _.e 3.. (a... eaten at- he? $432; 93 2. The temperature at the airport over a 10—hour period is given by f (t) = —t2 + 8! + 65 , 0 5 t 5 10. a. Find the average temperature. 3 2. I0 l *0 -— t 8%. flair: to J" (‘tz+5}fré5")d{: {'5 T4" T‘i- +égfjo --a 0 .. 3 _ — {Ep- ‘3 How. one.) --o = :55 "30% wows—o] l :— __ —£apo ,_ 4 —roco 3150 _ l 315 .2 +10 _ ..____ _, __ 0 _ 15‘ in. Find the minimum temperature. c. Find the maximum temperature. {NEE}: wafa-Q — Sit +9: 0 8‘ :At «(:11- tT—‘i—ad» va 3. Findthe area oftheregion bounded by thegraph of y=-x3+3x2+10x andthe x-axis. Sketch the graph and shade the region . Y:- - x0: "— 3; .4 a) ma: foo—(~K343ittoxiix+$g “—7‘3'X(X+Ll(K—5) .. I0 ( )3 L a (‘x3+3x“+mx}d “0’15 r“. —; x‘3“ “(Ok)dv+fr(wx3 L. k" . q 0 W=L~x3~5—XL|0+(-:LH 3 I: -1 27' + 5‘ +5384 ‘0 40’? Answers: 1a. P'(t)=20e‘ 4—20 1b. $440,259.32 1c.$44,025.93 2a. 713° 2b. 4s°att=1o 2c. 81°att=4 3. 407/4 ...
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