SuggestedProblemsWeek1and2

# SuggestedProblemsWeek1and2 - triples in 100 years 9 A...

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Suggested Problems for Week 1 and 2 1 First Order equations 1. Solve the equation y 0 = 6 y on ( -∞ , + ) 2. Solve y 0 = 5 y with the initial condition y (0) = 12. 3. Make a change of variables in order to solve y 00 + 17 y 0 = 0. 4. The population of a city grows at a rate that is proportional to the size of the population. If the population in 1970 was 125,000 and 140,000 in 1990, what is the expected population in 2010? 5. If 60% of a radioactive substance remains after 50 days, ﬁnd the decay constant (that is the constant λ in the equation Q 0 = - λQ ) and the half-life of the element. 6. Use a change of variables to solve y 0 = 2 y + 5. 7. A wooden tool is found to have a ratio (Carbon 14 over Carbon 12) that is only 0.1 of the corresponding ratio found in present-day living wood. Estimate the age of the tool. 8. If exponential growth is assumed, in how many years will a population double if it

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Unformatted text preview: triples in 100 years? 9. A radioactive substance with a half-life of 8 days is temporarily implanted in a hospital patient until 3/5 of the original amount remains. How long should the implant remain in the patient? 2 Separation of variables 1. solve y = ay by using the method of separation of variables. 2. solve y = 2 y + 5 by separation of variables. 3. solve y = 2 ty 2 4. solve y = y 3 .e t 5. solve y = e t-y with the initial condition that y (0) = 0 1 6. Newton’s law of cooling says that the temperature u ( t ) of an object satisﬁes u =-k ( u-T ) where T is the constant ambient temperature, and k is a positive constant. Find the temperature of the object at any time. 2...
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SuggestedProblemsWeek1and2 - triples in 100 years 9 A...

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