Calculus For The Life Sciences
2nd Edition
ISBN: 9780321964038
Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher: Pearson Addison Wesley,
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Question
Chapter 11.2, Problem 33E
To determine
To find:
The equation of Newton’s law of cooling by using method of solution of first order linear differential equation
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Check out a sample textbook solutionChapter 11 Solutions
Calculus For The Life Sciences
Ch. 11.1 - YOUR TURN 1 Find all solutions of the differential...Ch. 11.1 - Prob. 2YTCh. 11.1 - Prob. 3YTCh. 11.1 - YOUR TURN In Example 6, find the goat population...Ch. 11.1 - Find the general solution for each differential...Ch. 11.1 - Prob. 2ECh. 11.1 - Find the general solution for each differential...Ch. 11.1 - Prob. 4ECh. 11.1 - Prob. 5ECh. 11.1 - Prob. 6E
Ch. 11.1 - Find the general solution for each differential...Ch. 11.1 - Find the general solution for each differential...Ch. 11.1 - Find the general solution for each differential...Ch. 11.1 - Prob. 10ECh. 11.1 - Find the general solution for each differential...Ch. 11.1 - Find the general solution for each differential...Ch. 11.1 - Find the general solution for each differential...Ch. 11.1 - Find the general solution for each differential...Ch. 11.1 - Find the general solution for each differential...Ch. 11.1 - Find the general solution for each differential...Ch. 11.1 - Find the general solution for each differential...Ch. 11.1 - Find the general solution for each differential...Ch. 11.1 - Find the particular solution for each initial...Ch. 11.1 - Prob. 20ECh. 11.1 - Find the particular solution for each initial...Ch. 11.1 - Find the particular solution for each initial...Ch. 11.1 - Find the particular solution for each initial...Ch. 11.1 - Find the particular solution for each initial...Ch. 11.1 - Find the particular solution for each initial...Ch. 11.1 - Find the particular solution for each initial...Ch. 11.1 - Find the particular solution for each initial...Ch. 11.1 - Find the particular solution for each initial...Ch. 11.1 - Find the particular solution for each initial...Ch. 11.1 - Find the particular solution for each initial...Ch. 11.1 - Find the particular solution for each initial...Ch. 11.1 - Find the particular solution for each initial...Ch. 11.1 - Find the particular solution for each initial...Ch. 11.1 - Find the particular solution for each initial...Ch. 11.1 - Prob. 35ECh. 11.1 - Prob. 36ECh. 11.1 - Prob. 37ECh. 11.1 - Prob. 38ECh. 11.1 - Prob. 39ECh. 11.1 - Prob. 40ECh. 11.1 - Suppose that 0y0N. Let b=(Ny0)y0, and let...Ch. 11.1 - Prob. 42ECh. 11.1 - Tracer Dye The amount of a tracer dye injected...Ch. 11.1 - Soil Moisture The evapotranspiration index I is a...Ch. 11.1 - Fish Population An Isolated fish population is...Ch. 11.1 - Dieting A persons weight depends both on the daily...Ch. 11.1 - Refer to Exercise 46. Suppose someone initially...Ch. 11.1 - U.S. Hispanic Population A recent report by the...Ch. 11.1 - U.S Asian Population Refer to Exercise 50. The...Ch. 11.1 - Guernsey Growth The growth of Guernsey cows can be...Ch. 11.1 - Flea Beetles A study of flea beetles found that...Ch. 11.1 - Plant Growth Researchers have found that the...Ch. 11.1 - Spread of a Rumor Suppose the rate at which a...Ch. 11.1 - Radioactive Decay The amount of a radioactive...Ch. 11.1 - Newtons Law of Cooling Newtons law of cooling...Ch. 11.1 - According to the solution in Exercise 58 of the...Ch. 11.1 - Newtons Law of Cooling When a dead body is...Ch. 11.1 - Prob. 61ECh. 11.2 - Prob. 1YTCh. 11.2 - YOUR TURN Solve the initial value problem...Ch. 11.2 - Prob. 1ECh. 11.2 - Prob. 2ECh. 11.2 - EXERCISES Find the general solution for each...Ch. 11.2 - EXERCISES Find the general solution for each...Ch. 11.2 - EXERCISES Find the general solution for each...Ch. 11.2 - EXERCISES Find the general solution for each...Ch. 11.2 - EXERCISES Find the general solution for each...Ch. 11.2 - EXERCISES Find the general solution for each...Ch. 11.2 - EXERCISES Find the general solution for each...Ch. 11.2 - Prob. 10ECh. 11.2 - EXERCISES Find the general solution for each...Ch. 11.2 - Prob. 12ECh. 11.2 - Prob. 13ECh. 11.2 - Prob. 14ECh. 11.2 - EXERCISES Solve each differential equation,...Ch. 11.2 - EXERCISES Solve each differential equation,...Ch. 11.2 - EXERCISES Solve each differential equation,...Ch. 11.2 - EXERCISES Solve each differential equation,...Ch. 11.2 - EXERCISES Solve each differential equation,...Ch. 11.2 - EXERCISES Solve each differential equation,...Ch. 11.2 - Prob. 21ECh. 11.2 - Prob. 22ECh. 11.2 - Prob. 24ECh. 11.2 - Prob. 29ECh. 11.2 - Prob. 30ECh. 11.2 - Prob. 31ECh. 11.2 - Prob. 32ECh. 11.2 - Prob. 33ECh. 11.3 - Use Eulers method to approximate the solution of...Ch. 11.3 - Prob. 1ECh. 11.3 - Prob. 2ECh. 11.3 - Prob. 3ECh. 11.3 - Prob. 4ECh. 11.3 - Use Eulers method to approximate the indicated...Ch. 11.3 - Prob. 6ECh. 11.3 - Use Eulers method to approximate the indicated...Ch. 11.3 - Prob. 8ECh. 11.3 - Prob. 9ECh. 11.3 - Prob. 10ECh. 11.3 - Use Eulers method to approximate the indicated...Ch. 11.3 - Use Eulers method to approximate the indicated...Ch. 11.3 - Use Eulers method to approximate the indicated...Ch. 11.3 - Use Eulers method to approximate the indicated...Ch. 11.3 - Use Eulers method to approximate the indicated...Ch. 11.3 - Prob. 16ECh. 11.3 - Use Eulers method to approximate the indicated...Ch. 11.3 - Use Eulers method to approximate the indicated...Ch. 11.3 - Prob. 19ECh. 11.3 - Prob. 20ECh. 11.3 - Prob. 21ECh. 11.3 - Prob. 22ECh. 11.3 - Solve each differential equation and graph the...Ch. 11.3 - Prob. 28ECh. 11.3 - Prob. 29ECh. 11.3 - Prob. 31ECh. 11.3 - Immigration An island is colonized by immigration...Ch. 11.3 - Insect Population A population of insects y,...Ch. 11.3 - Whale Population Under certain conditions a...Ch. 11.3 - Goat Growth The growth of male Saanen goats can be...Ch. 11.3 - Spread of Rumors A rumor spreads through a...Ch. 11.4 - For Exercises 1-8, solve the system of...Ch. 11.4 - For Exercise 1-8, solve the system of differential...Ch. 11.4 - For Exercises 1-8, solve the system of...Ch. 11.4 - For Exercises 1-8, solve the system of...Ch. 11.4 - For Exercises 1-8, solve the system of...Ch. 11.4 - For Exercises 1-8, solve the system of...Ch. 11.4 - For Exercise 9-14, find the particular solution...Ch. 11.4 - Prob. 10ECh. 11.4 - Prob. 11ECh. 11.4 - Prob. 12ECh. 11.4 - For Exercise 9-14, find the particular solution...Ch. 11.5 - YOUR TURN Consider the system of differential...Ch. 11.5 - YOUR TURN Letting p=4,q=1,r=3,ands=5 in Example 2,...Ch. 11.5 - Prob. 9ECh. 11.5 - Whales and Krill For the system of differential...Ch. 11.5 - Prob. 12ECh. 11.5 - Prob. 13ECh. 11.5 - Prob. 17ECh. 11.5 - Prob. 18ECh. 11.6 - YOUR TURN 1 Suppose that an epidemic in a...Ch. 11.6 - Prob. 2YTCh. 11.6 - Spread of an Epidemic The native Hawaiians lived...Ch. 11.6 - Prob. 3ECh. 11.6 - Prob. 4ECh. 11.6 - Prob. 5ECh. 11.6 - Prob. 6ECh. 11.6 - Prob. 7ECh. 11.6 - Prob. 8ECh. 11.6 - Solve Exercise 10 if pure water is added instead...Ch. 11.6 - Prob. 14ECh. 11.6 - Solve Exercise 14 if a 25 solution of the same...Ch. 11.6 - Prob. 16ECh. 11.CR - Prob. 1CRCh. 11.CR - Prob. 2CRCh. 11.CR - Prob. 3CRCh. 11.CR - Prob. 4CRCh. 11.CR - Prob. 5CRCh. 11.CR - Prob. 6CRCh. 11.CR - Prob. 7CRCh. 11.CR - Prob. 8CRCh. 11.CR - Prob. 9CRCh. 11.CR - Prob. 10CRCh. 11.CR - Prob. 11CRCh. 11.CR - Prob. 12CRCh. 11.CR - Prob. 13CRCh. 11.CR - Prob. 14CRCh. 11.CR - Prob. 15CRCh. 11.CR - Prob. 16CRCh. 11.CR - Prob. 17CRCh. 11.CR - Prob. 18CRCh. 11.CR - Prob. 19CRCh. 11.CR - Classify each equation as separable, linear, both...Ch. 11.CR - Prob. 21CRCh. 11.CR - Prob. 22CRCh. 11.CR - Prob. 23CRCh. 11.CR - Prob. 24CRCh. 11.CR - Prob. 25CRCh. 11.CR - Prob. 26CRCh. 11.CR - Prob. 27CRCh. 11.CR - Prob. 28CRCh. 11.CR - Prob. 29CRCh. 11.CR - Prob. 30CRCh. 11.CR - Prob. 31CRCh. 11.CR - Prob. 32CRCh. 11.CR - Prob. 33CRCh. 11.CR - Prob. 34CRCh. 11.CR - Prob. 35CRCh. 11.CR - Prob. 36CRCh. 11.CR - Prob. 37CRCh. 11.CR - Prob. 38CRCh. 11.CR - Prob. 39CRCh. 11.CR - Prob. 40CRCh. 11.CR - Prob. 41CRCh. 11.CR - Prob. 42CRCh. 11.CR - Prob. 43CRCh. 11.CR - Prob. 44CRCh. 11.CR - Prob. 45CRCh. 11.CR - Prob. 46CRCh. 11.CR - Prob. 47CRCh. 11.CR - Prob. 48CRCh. 11.CR - Prob. 49CRCh. 11.CR - Prob. 50CRCh. 11.CR - Prob. 51CRCh. 11.CR - Prob. 52CRCh. 11.CR - Solve each of the following systems of...Ch. 11.CR - Prob. 54CRCh. 11.CR - Effect of Insecticide After use of an experimental...Ch. 11.CR - Growth of a Mite Population A population of mites...Ch. 11.CR - Prob. 60CRCh. 11.CR - Prob. 61CRCh. 11.CR - Prob. 68CRCh. 11.CR - Prob. 69CRCh. 11.CR - Prob. 70CRCh. 11.CR - Prob. 71CRCh. 11.EA - Prob. 1EACh. 11.EA - Prob. 2EACh. 11.EA - Prob. 3EACh. 11.EA - Prob. 5EACh. 11.EA - Prob. 7EACh. 11.EA - Prob. 8EA
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- Newtons Law of Cooling Newtons law of cooling states that the rate of change of temperature of an object is proportional to the difference in temperature between the object and the surrounding medium. Thus, if T is the temperature of the object after t hours and TM is the constant temperature of the surrounding medium, then dTdt=k(TTM) where k is a constant. Use this equation in Exercises 58-61. Show that the solution of this differential equation is T=Cekt+TM where C is a constant.arrow_forwardDefine Newton’s Law of Cooling. Then name at least three real-world situations where Newton’s Law of Cooling would be applied.arrow_forwardElectricity In a series resistance-capacitance DC circuit, the instantaneous charge Q on the capacitor as a function of time where t=0 is the moment the circuit is energized by closing a switch is given by the equation Qt=CV1-e-t/RC, where C,V, and R are constants. Further, the instantaneous charging current Ic is the rate of chage of charge on the capacitor, or Ic=dQ/dt. Source: Kevin Friedrich. a. Find the expression for Ic as a function of time. b. If C=10-5 farads, R=107 ohms, and V=10 volts, what is the vharging current after 200 seconds? Hint: When placed into the function in part a, the units can be combined into amps.arrow_forward
- Multivariable Calculus Total Differentials and Approximations LIFE SCIENCE APPLICATIONS Blood Volume In Exercise 52 of Section 2 in this chapter, we found that the number of liters of blood pumped through the lungs in one minute is given by C=bav Suppose a=160,b=200 and v=125. Estimate the change in C if a becomes 145,b becomes 190, and v changes to 130.arrow_forwardFlea Beetles A study of flea beetles found that the change in the rate of flea beetles moving in and out of a patch of beetles could be described by the differential equation dNdt=mN+i where N is the number of beetles in a patch, m is the rate at which beetles move out of the patch, and i is the rate at which they move in. Source: Ecological Monographs. a. Solve the differential equation above with the initial condition N(0)=N0. b. After the researchers cleared a patch of beetles, so that N0, they would return 8 hours later and count the number of beetles. Show that the parameter i can then be estimated by the equation i=mN(8)e8m1 c. The researchers estimated m using the equation m=lnFsd, where Fsd is the fraction of beetles who remained in the patch in which they were released. For the beetles P, striolata released in July in the lush interior of patches 5 meters apart, the average values of Fsd and N(8) were 0.709 and 4.5, respectively. Find the values of m and i.arrow_forwardMultivariable Calculus Total Differentials and Approximations LIFE SCIENCE APPLICATIONS Heat Loss In Exercise 50 of Section 2 of this chapter, we found that the rate of heat loss in watts in harbor seal pups could be approximated by H(m,T,A)=15.2m0.67(TA)10.23lnm10.74 Where m is the body mass of the pup in kg, and T and A are the body core temperature and ambient water temperature, respectively in C. Suppose m is 25kg, T is 36.0, and A is 12.0, Approximate the change in H if m changes to 26kg,T to 36.5 and A to 10.0.arrow_forward
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