Problem 1E: The population of a community is known to increase at a rate proportional to the number of people... Problem 2E: Suppose it is known that the population of the community in Problem 1 is 10,000 after 3 years. What... Problem 3E: The population of a town grows at a rate proportional to the population present at time t. The... Problem 4E: The population of bacteria in a culture grows at a rate proportional to the number of bacteria... Problem 5E: The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at time... Problem 6E: Initially 100 milligrams of a radioactive substance was present. After 6 hours the mass had... Problem 7E: Determine the half-life of the radioactive substance described in Problem 6. 6. Initially 100... Problem 8E: Consider the initial-value problem dA/dt = kA, A(0) = A0 as the model for the decay of a radioactive... Problem 9E: When a vertical beam of light passes through a transparent medium, the rate at which its intensity I... Problem 10E: When interest is compounded continuously, the amount of money increases at a rate proportional to... Problem 11E: Carbon Dating Archaeologists used pieces of burned wood, or charcoal, found at the site to date... Problem 12E: The Shroud of Turin, which shows the negative image of the body of a man who appears to have been... Problem 13E: Newtons Law of Cooling/Warming A thermometer is removed from a room where the temperature is 70 F... Problem 14E: A thermometer is taken from an inside room to the outside, where the air temperature is 5 F. After 1... Problem 15E: A small metal bar, whose initial temperature was 20 C, is dropped into a large container of boiling... Problem 16E: Two large containers A and B of the same size are filled with different fluids. The fluids in... Problem 17E: A thermometer reading 70 F is placed in an oven preheated to a constant temperature. Through a glass... Problem 18E: At t = 0 a sealed test tube containing a chemical is immersed in a liquid bath. The initial... Problem 19E: A dead body was found within a closed room of a house where the temperature was a constant 70 F. At... Problem 20E: The rate at which a body cools also depends on its exposed surface area S. If S is a constant, then... Problem 21E: A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine containing 1 gram... Problem 22E: Solve Problem 21 assuming that pure water is pumped into the tank. 21. A tank contains 200 liters of... Problem 23E: A large tank is filled to capacity with 500 gallons of pure water. Brine containing 2 pounds of salt... Problem 24E: In Problem 23, what is the concentration c(t) of the salt in the tank at time t? At t = 5 min? What... Problem 25E: Solve Problem 23 under the assumption that the solution is pumped out at a faster rate of 10... Problem 26E: Determine the amount of salt in the tank at time t in Example 5 if the concentration of salt in the... Problem 27E: A large tank is partially filled with 100 gallons of fluid in which 10 pounds of salt is dissolved.... Problem 28E: In Example 5 the size of the tank containing the salt mixture was not given. Suppose, as in the... Problem 29E: A 30-volt electromotive force is applied to an LR-series circuit in which the inductance is 0.1... Problem 30E Problem 31E: A 100-volt electromotive force is applied to an RC-series circuit in which the resistance is 200... Problem 32E: A 200-volt electromotive force is applied to an RC-series circuit in which the resistance is 1000... Problem 33E: An electromotive force E(t)={120,0t200,t20 is applied to an LR-series circuit in which the... Problem 34E: An LR-series circuit has a variable inductor with the inductance defined by L(t)={1110t,0t100,t10.... Problem 35E: Air Resistance In (14) of Section 1.3 we saw that a differential equation describing the velocity v... Problem 36E: How High?No Air Resistance Suppose a small cannonball weighing 16 pounds is shot vertically upward,... Problem 37E: How High?Linear Air Resistance Repeat Problem 36, but this time assume that air resistance is... Problem 38E: Skydiving A skydiver weighs 125 pounds, and her parachute and equipment combined weigh another 35... Problem 39E: Rocket Motion Suppose a small single-stage rocket of total mass m(t) is launched vertically, the... Problem 40E: Rocket MotionContinued In Problem 39 suppose of the rockets initial mass m0 that 50 kg is the mass... Problem 41E: Evaporating Raindrop As a raindrop falls, it evaporates while retaining its spherical shape. If we... Problem 42E Problem 43E Problem 44E: Constant-Harvest model A model that describes the population of a fishery in which harvesting takes... Problem 45E: Drug Dissemination A mathematical model for the rate at which a drug disseminates into the... Problem 46E: Memorization When forgetfulness is taken into account, the rate of memorization of a subject is... Problem 47E: Heart Pacemaker A heart pacemaker, shown in Figure 3.1.15, consists of a switch, a battery, a... Problem 48E: Sliding Box (a) A box of mass m slides down an inclined plane that makes an angle with the... Problem 49E: Sliding Box—Continued
In Problem 48 let s(t) be the distance measured down the inclined plane from... Problem 50E: What Goes Up (a) It is well known that the model in which air resistance is ignored, part (a) of... format_list_bulleted