Test 3B - Math 241 Test #3 Version 13 Textbook 7.4 through...

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Unformatted text preview: Math 241 Test #3 Version 13 Textbook 7.4 through 8.1 *No calculators, No cell phones, No PDAs *No questions during the test unless there is a typing error *Please begin each problem at the top of a new page in the blue book *Please do not leave if you have to pass over someone in your row; wait until group “leave” times are announced. *Show all work. Mark out any work that you do not want graded. . . .. . . dP P l. The logistic dll'ferenual equatlon — = .4P(l— dr 1000 models the rate at which people are hearing about a rumor Ptt) over time t, expressed in hours. in an isolated town. a. (6 points) Make a sketch of the solution to the differential equation. b. (3 points) At what population size does the concavity in your graph of PU) change? Recall your Maple Lab! c. (3 points) Which function listed below could be a general solution to the differential equation? A is a constant. . _ 1000 Pr=A'4’ ‘iPr=—~ 1) t) e 1) t) HMA, ) P(0):2 iii) PU) = IOOO — Ae'm 2. Assume a radioactive element decays at a rate proportional to the amount present at any time. Let the variable A stand for the amount in grams of the radioactive substance at time t, measured in minutes. a. (4 points)Write this as a differential equation. b. (4 points) When there are 50 grams of substance A, the element is decaying at a rate of 10 grams per minute. Use this information to find the decay constant. c. (4 points) If the initial amount ofthe substance is 100 grams, state the solution‘function . A“). to your differential equation. 3. (20 points) Solve the following initial value problem. y"+4y'+4r=0 y(0)=0 y(l)=3 4.(20 points) Solve the following differential equation. Find the general solution function. y" + y = sinx Continue on next page please. Lying If. .-" 1"} I} 5. A spring with a 2kg mass has natural length 3m and is maintained stretched to length of 5m by a force of 24N. The damping constant is 14 . The spring is stretched to a length 7 m and then released with velocity 1 m/sec. Let x(t) be the position of the mass at time t seconds. a. (3 pts) Find the spring constant . b. (5 pts)Write the differential equation for this problem. DO NOT solve it. c. (2 pts) Write the initial conditions. (1. (5 pts) Without solving the differential equation, what type of damping (overdarnping, critical damping or underdamping) is present here? Support your answer. 6. List the first three terms of each sequence. Determine whether the following sequences converge or diverge. If the sequence converges, find the limit. . (-1)” a)(7 pomts) a" = n 2 b) (7 points) a" = "‘ *1 4n ln(nl c) (7 points) a" = H, _/ f- ._I, , 5 , K H +171 / :— ®i 9+4; 0 W"0 2"”:3 p + 4r- + LVL ’0 '2. 3+3) =0 T 3 "2—- doubfle roo+ a ’7’ ‘wp—M—‘T )3); . ’x—kCfixXébc #3382066 (Low 5 C, 80+ ca = C2 g'éfi-.a O :— c,(1)+c?,(o\ 3 gala}? O 5 Of 333: c, gig. e°x(c, aux 4— C; (WHO A.~ u A C, 69¢X -+ C‘;AénX“‘“~ k . __.._.r-- 1 i i qLerr‘ns . 4' A ' 4cmx+ Bémx m““" 13°” 5”” ' v A .. B 2 x a“? 753.0 ' X ALWX-é Am ‘ = Axcwxqb Bacamx “WM A - W 3 mm” 7L 6mm / .. 4 77” SI)” +74 €05¥ 'f BXMSX +fif/fiy W /l ’l { ‘ 42%;;22 + Wm 550% W ’ ‘* +-- H VLAJ'Wofi 6 “‘ Com‘f‘. @ b7 11 x” + “@5319 a.) r) M" ouan £24.42ng 3hr, mun-mych 49 5m .493, qux/ F /4 x =9 11*” Q“? r v ‘\ (W s»; y— .— + cad/f fix: 0 // m 76 ewe—MMQ +9 0» Eff”) 0'3". L/m bfionDL e fiu‘a 1‘1 Wm r~ ’ a a" "P Mk C0 .r C) QFL-‘t‘ Mr + ML ~— 0 r fwflwm’ ' “ *' ‘ fluff 3?“. m ‘ r” ’ " '7Z..." / 1’ / an a W- WWWW w»_ W_' 52 read rdo+§ L . *9 I fl I!“ I, \ a fi WW " r’ F‘ (,1 V. x .4... 3 y. "3’ .. ‘ ,x -y.‘ g 3 (J g; _... _./_‘2. 7 5’ 2 A; J J 7— K) r '2 1r (/o/i mug—44 #32 J K J ’ 3 .w % in} .x 3 " ...
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Test 3B - Math 241 Test #3 Version 13 Textbook 7.4 through...

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