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t l o ﬂat: 4/2}? n. m ._ A ' See handom‘ 0F problems #ﬂéﬂﬂ’ﬂ/S/b
79000 W M Exam/Egg and Woo/ems 90°F is stood in
temperature is 50°F After 5 'me If, m minmetsl denote the ﬁ : k TS
T‘S
~TS m U“: LL: (3) Write a differential equation for H(t) using New d
_r' ‘E ton 3 Law of Cooling. 0’“ 0’ (b) Solve the differential e uat
c: C: C: l q 1011. x I g
m E E: t (C) When Will the temperature oftherice have dropped % OilSCUSS ‘ ’
PM ro6o°F7 01c K (9 (,UOHS
i S S gr 3 {9‘ n I 7 f: (gr llsrtnj Var/ab 6 3 
\
£9
(9 According to a simple physiological model, an athletic r
adult needs 20 calories per day per pound of body weight % {g aLJL
to maintain his weight. If he consumes more or fewer . __ calories than those required to maintain his weight, his weight changes at a rate proportional to the difference
between the number of calories consumed and the num
ber needed to maintain his current weight; the constant
/\ 1c amouni‘
ofproportionality is 1/3500 pounds per calorie. Suppose a O 2 K  #0
that a particular person has a constant caloric intake of m I calories per day. Let W’(t) be the person’s weight in pounds at time 25 (measured in days). (a) What differential equation has solution WU)?
(b) Solve this differential equation. l ( ,_ >
(c) Graph W'(t) if the person starts out weighing 160 M I I w
pounds and consumes 3000 calories a day. 35 I 9(6) : dear/’9 7. Water leaks out of a barrel at a rate proportional to the
square root of the depth of the water at that t1me. If the water level starts at 36 inches and drops to 35 inches in l I : ._ k ’lfy" J k hour, how long will it take for all of the water to leak out ‘ of the barrel? 94 d/scags 507/73 50 SHEETS
mo SHEETS 224 443 200 SHEETS 22—141
221412 mm,”
/,/ Co /. .‘BsC‘i
M
\ b AppltcatLQD§_1§iKJQQde/mg  M. i 1 A spherical snowball melts at a rate proportional to its surface area. — ‘ 7.
Asiath ' LI‘TH"
' ' ‘ ' ' V.
( ) Write a differential equation for its volume, . 1— 3/
(1:) If the initial volume is V0, solve the differential V  3 equation and graph the solution.
(c) When does the snowball disappear? 7 7 77 7 I” W We're told OW/d—t = KH ) Er K70. To WNTO TWS In Terms 013 GHQ ‘H’le 1 \li anohi by subsnrtm'on.
E %
$15 = “ktAr = I<(H‘TWZ)= l< (LHT) It b 2cm 6 Aspheye, [i use V sphere g‘Theteq‘t/m Q! = k VZ/3 where, R has been
' CV5 renamed (Ks k(47r)'/337/3) A chemical reaction involves one molecule of a sub
stance A combining with one molecule of substance B to
form one molecule of substance C, written A + B —+ C. 0
The Law of Mass Action states that the rate at which C OF @ ta 1
is formed is proportional to the product of the quantities H I ,
of A and B present. Assume a and b are the initial quan a A X
tities of A and B, and 2: is the quantity of C present at time t. (3) Write a differential equation for z. 6 @ ’hm‘t: (b) Solve the equation with z(0) = 0.
t\ b,“ x“ a; ram 010 ﬁrmanbn ot a = K (@uamtg at: AMQuantrg 0:116) d _ ,
3.1% I k(0t—><)Cb><7 . If the initial quantities, a and b, in Problem 15 are the
‘ same, write and solve a differential equation for it, with
2(0) = O. 7/ g};— = k (0H0 (0H) ...
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This note was uploaded on 03/26/2012 for the course MAC 2312 taught by Professor Bonner during the Fall '08 term at University of Florida.
 Fall '08
 Bonner
 Calculus

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