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'Ytl  (1"(6) 2: 906?.  Sf(ciloOclﬂ: «5th — 3f—10+;1t F‘ée) ~— ao ENE—t "9.0 b. Find the total profit forthe first 10 days. .
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100906 —fAa)d{:aoe ""r “—104: :20: w
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7—206 _ 50‘ Aoowao = oZ’Oe' —.;t’?'o :_ 3990 2.59 3.1
c. Find the average daily proﬁt for the ﬁrst 10 days. '10 _ .. HQ ‘
w. _.e 3.. (a... eaten at he? $432; 93 2. The temperature at the airport over a 10—hour period is given by f (t) = —t2 + 8! + 65 , 0 5 t 5 10.
a. Find the average temperature. 3 2. I0
l *0 — t 8%.
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— {Ep ‘3 How. one.) o = :55 "30% wows—o]
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:— __ —£apo ,_ 4 —roco 3150 _ l 315 .2
+10 _ ..____ _, __ 0 _ 15‘
in. Find the minimum temperature. c. Find the maximum temperature.
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3. Findthe area oftheregion bounded by thegraph of y=x3+3x2+10x andthe xaxis.
Sketch the graph and shade the region . Y:  x0: "— 3; .4 a)
ma: foo—(~K343ittoxiix+$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—XL0+(: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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 Spring '10
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