Download Test 2 with Solution for Brief Survey of Calculus 2 | MATH and more Exams Mathematics in PDF only on Docsity! M120 TEST 2 PRINT NAME
Spring, 2011 ——. ..
THIS TEST IS WORTH 50 POINTS
PORTION SCORE (for instructor's use only)
Multiple-choice 6
Show-your-work f /
TOTAL od iy
SHOW-YOUR-WORK INSTRUCTIONS: For each “show-your-work” question, work out
your solution and write your final answer in the space below, clearly and legibly.
PLEASE ROUND ALL NUMERICAL ANSWERS TO TWO DECIMAL PLACES!
PROBLEM 08: Suppose the variable f = the amount of time required to finish your
calculus homework has the following density function:
p(t) = 4t-4t®, for O<ts 1 hour, and p(t) = 0 elsewhere.
a.) Find the probability that it takes you betwee 15 and 45 minutes to finish your
homework. 3 2 “ a
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b.) Find the Cumulative Distribution Function of t, P(t).
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c.) Using the Cumulative Distribution Function, find the probability that it takes you at
least 40 minutes to complete your homework.
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d.) Find the mean amount of time it takes you to finish your homework.
PROBLEM 10: The rate at which a rumor spreads is proportional to the current number
of people who have heard the rumor.
Let P(t) = number of people who have heard the rumor t days after rumor starts.
a.) Write a differential equation that is satisfied by P(t).
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b.) Write the general solution to the equation found in part a. (if there are parameters of
the function that are unknown, you may leave them as unknowns in the solution).
c.) If 25 people have heard the rumor at t 0, write the specific solution to tha differential
equation found in part b. .
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d.) If, in addition, 68 people have heard the rumor at t = 2 days after it started, how many
days after it started will it take before 400 people have heard the rumor?
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PROBLEM 11: The rate at which a thermos full of coffee is cooling off is proportional to
the difference between the temperature of the thermos and the temperature of
surrounding room. The thermos starts out at 140 degrees Fahrenheit, and the
surrounding room is at a constant 68 degrees Fahrenheit.
Let F(t) = temperature of the thermos t minutes after entering room.
a.) Write a differential equation for this situation satisfied by F(t).
b.) Write the general solution to the differential equation found in part a.
c.) If the temperature of the thermos 10 minutes after bringing it into the room is 110
degrees Fahrenheit, what will the temperature of the thermos be at t = 30 minutes after
entering the room?
d.) If the temperature of the coffee was 180 degrees when the coffee was poured into
the thermos, how many minutes before entering the room was the coffee poured into the
thermos? (assume that the coffee is losing temperature at the same rate before entering
the room as itis after entering the room)
