125 3/4/12
Math HW_9C
W bA ign
Math 125 HW_9C (Home ork) Current Score : 55 / 80 Due : Sunday, March 4 2012 11:00 PM PST
MARIO C EASER JR FIGUEROA Math 125 Winter 2012, section B, Winter 2012 Instructor: Neal Koblitz
1. 12/12 points | Previous Answers
SC alcET7 3.8.003.
A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has increased to 250. (a) Find an expression for the number of bacteria after t hours.
P(t) = (b) Find the number of bacteria after 2 hours. (Round your answer to the nearest whole number.) P(2) = 625 bacteria
(c) Find the rate of growth after 2 hours. (Round your answer to the nearest whole number.) P'(2) = 573 bacteria per hour
(d) When will the population reach 10,000? (Round your answer to one decimal place.) t = 5.0 hr
2. 6/6 points | Previous Answers
SC alcET7 3.8.010.
A sample of a radioactive substance decayed to 96% of its original amount after a year. (Round your answers to two decimal places.) (a) What is the half-life of the substance? 16.98 yr
(b) How long would it take the sample to decay to 10% of its original amount? 56.41 yr
3. 5/5 points | Previous Answers
SC alcET7 3.8.011.
Scientist can determine the age of ancient objects by a method called radiocarbon dating. The
. ebassign.net/ eb/Student/Assignment-Responses/submit?dep=3947464#Q9 1/5
3/4/12
Math 125 HW_9C
bombardment of the upper atmosphere by cosmic rays converts nitrogen to a radioactive isotope of carbon, 14C, with a half-life of about 5730 years. Vegetation absorbs carbon dioxide through the atmosphere and animal life assimilates 14C through food chains. When a plant or animal dies, it stops replacing its carbon and the amount of 14C begins to decrease through radioactive decay. Therefore, the level of radioactivity must also decay exponentially. A parchment fragment was discovered that had about 68% as much 14C radioactivity as does plant material on Earth today. Estimate the age of the parchment. (Round your answer to the nearest hundred years.) 3200 yr
4. 6/6 points | Previous Answers
SC alcET7 3.8.013.MI.
A roast turkey is taken from an oven when its temperature has reached 185F and is placed on a table in a room where the temperature is 75F. (Round your answers to the nearest whole number.) (a) If the temperature of the turkey is 150F after half an hour, what is the temperature after 60 minutes? T(60) = 126 F
(b) When will the turkey have cooled to 110? t = 90 min
5. 6/6 points | Previous Answers
SC alcET7 3.8.015.
When a cold drink is taken from a refrigerator, its temperature is 5C. After 25 minutes in a 20C room its temperature has increased to 10C. (Round your answers to two decimal places.) (a) What is the temperature of the drink after 60 minutes? 14.33 C
(b) When will its temperature be 14C? 56.50 min
. ebassign.net/ eb/Student/Assignment-Responses/submit?dep=3947464#Q9
2/5
3/4/12
Math 125 HW_9C
6. 2/10 points | Previous Answers
Suppose you drop a stone of mass m from a great height in the earth's atmosphere, and the only forces acting on the stone are the earth's gravitational attraction and a retarding force due to air resistance, which is proportional to the velocity the differential equation m d = mg k dt is positive pointing down, k is a positive constant, and g > 0 is the (constant) . Then, since F = m a and a = d /dt, we have
where for g.)
acceleration due to gravity. (Throughout this problem, just use "g"; do not put in a numerical value
(a) The stone is dropped, so what is (0) =
(0)?
(b) Find
as a function of t. (t) = (your answer will depend on g, k, m, and t)
(c) Find lim
t
(t) = (your answer will depend on g, k, and m)
7. points 12/12 | Previous Answers
Experimenting, you have found that 12 ounces of 180F coffee in your favorite cup will take 20 minutes to cool to a drinking temperature of 110F in a 70F room. Assume that when you add cream to the coffee, the two liquids are mixed instantly, and the temperature of the mixture instantly becomes the weighted average of the temperature of the coffee and of the cream (weighted by the number of ounces of each fluid). Also assume that the cooling constant of the liquid (the constant k in the equations on p. 237 in section 3.8 for Newton's Law of Cooling) does not change when you add the cream. (a) If you add 2 ounces of 40F cream to the 180F coffee in the cup, how long will it take for the mixture to reach drinking temperature? Give your answer (in minutes) in decimal form with at least 3 decimal digits (for example, 12.345 minutes). 16.033 minutes
(b) If you let the 12 ounces of 180F coffee cool for 5 minutes before adding 2 ounces of 40F cream, how long will it take (after the initial time when the coffee was 180F) for the mixture to
. ebassign.net/ eb/Student/Assignment-Responses/submit?dep=3947464#Q9 3/5
3/4/12
Math 125 HW_9C
reach drinking temperature? Give your answer (in minutes) in decimal form with at least 3 decimal digits (for example, 12.345 minutes). 15.760 minutes
(c) In order to reach drinking temperature as quickly as possible, should you add the cream immediately, or wait 5 minutes? you should add the cream immediately you should wait 5 minutes
8. 6/14 points | Previous Answers
This problem models pollution effects in the Great Lakes. We assume pollutants are flowing into a lake at a constant rate of I kg/year, and that water is flowing out at a constant rate of F km3/year. We also assume that the pollutants are uniformly distributed throughout the lake. If C(t) denotes the concentration (in kg/km3) of pollutants at time t (in years), then C(t) satisfies the differential equation dC = dt F C + I, V V
where V is the volume of the lake (in km3). We assume that (pollutant-free) rain and streams flowing into the lake keep the volume of water in the lake constant. (a) Suppose that the concentration at time t = 0 is C0. Determine the concentration at any time t by solving the differential equation.
C(t) = (to enter C0 in your answer, type "C_0", that is, "capital C, underscore, zero")
(b) Find lim C(t) =
t
(c) For Lake Erie, V = 458 km3 and F = 175 km3/year. Suppose that one day its pollutant
. ebassign.net/ eb/Student/Assignment-Responses/submit?dep=3947464#Q9 4/5
3/4/12
Math 125 HW_9C
concentration is C0 and that all incoming pollution suddenly stopped (so I = 0). Determine the number of years it would then take for pollution levels to drop to C0/10. Give your answer in decimal form, rounded to the nearest year. 6 years
(d) For Lake Superior, V = 12221 km3 and F = 65.2 km3/year. Answer the same question as in part (c) for Lake Superior. 16 years
9. /9 points
A person borrows $10,000 and repays the loan at the rate of $2,400 per year. The lender charges interest of 10% per year. Assuming the payments are made continuously and interest is compounded continuously (a pretty good approximation to reality for long-term loans), the amount M(t) of money (in dollars) owed t years after the loan is made satisfies the differential equation dM = 1 M 2400 dt 10 and the initial condition M(0) = 10000. (a) Solve this initial-value problem for M(t).
M(t) = (b) How long does it take to pay off the loan? That is, at what time t is M(t) = 0? Give your answer (in years) in decimal form with at least 3 decimal digits. years
. ebassign.net/ eb/Student/Assignment-Responses/submit?dep=3947464#Q9
5/5