Problem 1CYU: a. Solve the differential equation P(t)=0.6P(t),P(0)=50. b. Solve the differential equation... Problem 2CYU: Under ideal conditions a colony of Escherichia coli bacteria can grow by a factor of 100 every 2... Problem 1E: In Exercises 110, determine the growth constant k, then find all solutions of the given differential... Problem 2E: In Exercises 110, determine the growth constant k, then find all solutions of the given differential... Problem 3E: In Exercises 110, determine the growth constant k, then find all solutions of the given differential... Problem 4E: In Exercises 110, determine the growth constant k, then find all solutions of the given differential... Problem 5E: In Exercises 110, determine the growth constant k, then find all solutions of the given differential... Problem 6E: In Exercises 110, determine the growth constant k, then find all solutions of the given differential... Problem 7E: In Exercises 110, determine the growth constant k, then find all solutions of the given differential... Problem 8E: In Exercises 110, determine the growth constant k, then find all solutions of the given differential... Problem 9E: In Exercises 110, determine the growth constant k, then find all solutions of the given differential... Problem 10E: In Exercises 110, determine the growth constant k, then find all solutions of the given differential... Problem 11E: In Exercises 1118, solve the given differential equation with initial condition. y=3y,y(0)=1. . Problem 12E: In Exercises 1118, solve the given differential equation with initial condition. y=4y,y(0)=0. . Problem 13E: In Exercises 1118, solve the given differential equation with initial condition. y=2y,y(0)=2. . Problem 14E: In Exercises 1118, solve the given differential equation with initial condition. y=y,y(0)=4. . Problem 15E: In Exercises 1118, solve the given differential equation with initial condition. y0.6y=0,y(0)=5. . Problem 16E: In Exercises 1118, solve the given differential equation with initial condition. yy7=0,y(0)=6. . Problem 17E: In Exercises 1118, solve the given differential equation with initial condition. 6y=y,y(0)=12. . Problem 18E: In Exercises 1118, solve the given differential equation with initial condition. 5y=3y,y(0)=7. . Problem 19E: Population and Exponential Growth Let P(t) be the population (in millions) of a certain city t years... Problem 20E: Growth of a Colony of Fruit Flies A colony of fruit flies exhibits exponential growth. Suppose that... Problem 21E: GrowthConstant for a Bacteria Culture Abacteria culture that exhibits exponential growth quadruples... Problem 22E: Growth of a Bacteria Culture The initial size of a bacteria culture that grows exponentially was... Problem 23E: Using the Differential Equation Let P(t) be the population (in millions) of a certain city t years... Problem 24E: Growth of Bacteria Approximately 10,000 bacteria are placed in a culture. Let P(t) be the number of... Problem 25E: Growth of cells After t hours, there are P(t) cells present in a culture, where, P(t)=5000e0.2t a.... Problem 26E: Insect Population The size of a certain insect population is given by P(t)=300e0.01t, where t is... Problem 27E: Population Growth Determine the growth constant of a population that is growing at a rate... Problem 28E: Time to Triple Determine the growth constant of a population that is growing at a rate proportional... Problem 29E: Exponential Growth A population is growing exponentially with growth constant 0.05. In how many... Problem 30E: Time to DoubleA population is growing exponentially with growth constant 0.04. In how many years... Problem 31E: Exponential Growth The rate of growth of a certain cell culture is proportional to its size. In 10... Problem 32E: Worlds Population The worlds population was 5.51 billion on January 1,1993, and 5.58 billion on... Problem 33E Problem 34E: A Population Model The population (in millions) of a state t years after 2010 is given by the graph... Problem 35E: Radioactive Decay A sample of 8 grams of radioactive material is placed in a vault. Let P(t) be the... Problem 36E: Radioactive Decay Radium 226 is used in cancer radiotherapy. Let P(t) be the number of grams of... Problem 37E: Decay of Penicillin in the Bloodstream A person is given an injection of 300 milligrams of... Problem 38E: Radioactive Decay Ten grams of a radioactive substance with decay constant 0.04 is stored in a... Problem 39E: Radioactive Decay The decay constant for the radioactive element cesium 137 is 0.023 when time is... Problem 40E: Drug ConstantRadioactive cobalt 60 has a half-life of 5.3 years. Find its decay constant. Problem 41E: Iodine Level in Dairy Products If dairy cows eat hay containing too much iodine 131, their milk will... Problem 42E: Half-Life Ten grams of a radioactive material disintegrates to 3 grams in 5 years. What is the... Problem 43E: Decay of Sulfate in the Bloodstream In an animal hospital, 8 units of a sulfate were injected into a... Problem 44E: Radioactive Decay Forty grams of a certain radioactive material disintegrates to 16 grams in 220... Problem 45E: Radioactive Decay A sample of radioactive material decays over time (measured in hours) with decay... Problem 46E: Rate of Decay A sample of radioactive material has decay constant .25, where time is measured in... Problem 47E: Carbon Dating In 1947, a cave with beautiful prehistoric wall paintings was discovered in Lascaux,... Problem 48E: King Arthur's Round Table According to legend, in the fifth century King Arthur and his knights sat... Problem 49E Problem 50E: Population of the PacificNorthwest In 1938, sandals woven from strands of tree bark were found in... Problem 51E: Time of the Fourth Ice Age Many scientists believe there have been four ice ages in the past 1... Problem 52E: Time Constant Let T be the time constant of the curve y=Cet as defined in Fig. 5. Show that T=1/.... Problem 53E Problem 54E: Time Constant and Half-life Consider as exponential decay function P(t)=P0et, and let T denote its... Problem 55E: An Initial Value Problem Suppose that the function P(t) satisfies the differential equation... Problem 56E: Time to Finish Consider the exponential decay function y=P0et, with time constant T. We define the... format_list_bulleted