DIFFERENTIAL EQUATIONS, Exams of Differential Equations

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SAMPLE PROBLEM 1: Radium decomposes in air at the rate proportional to the present amount. If initially there are 20 grams, and after 10 years, 0.6% of the original amount decomposed: a) Set a model that will predict the amount of radium at an’ ie t. b) r Eira c) Whati s the amount =— in 900 years? SAMPLE PROBLEM 2: Radium decomposes in air at the rate proportional to the amount present. It is found out that in 25 years, 1.1% of a certain amount decomposed. Determine approximately how long will it take: a) For one-half of the| mount to decompose? b) 20% of the amount to decompose c) What percent of the amount will decompose in 50 years? ypu Li SAMPLE PROBLEM 3: The population of the town grows at the rate proportional to the population present at any time t. The initial population of 500 increases by 15% in 10 years. What will be the population in 30 years? SAMPLE PROBLEM 1: A thermometer reading 10 degrees celsius is brought in a room whose temperature is 18 degrees celsius. One minute later, the thermometer reading is 14 degrees celsius. How long does it take until the reading becomes 16 degrees celsius? ai SAMPLE PROBLEM 2: A metal is heated up to a temperature of 500 degrees celsius. It is then exposed to a temperature of 38 degrees celsius. After 2 minutes, the temperature of the metal becomes 190 degrees celsius. When will the temperature be 100 degrees celsius? What is the temperature after 4 minutes? SAMPLE PROBLEM 3: A thermometer is taken from an inside room to the outside, where the air temperature is 5 degrees farenheit. After 1 minute, the thermometer reads 55 degrees F and after 5 minutes it reads 30 degrees F. What was the initial temperature of the thermometer when inside the room?