Applications of differential equations 1. A certain radioactive material follows the law of exponential growth. If between noon and 2 pm the population triples, at what time should thepopulation become 100 times what it was at noon?2. A thermometer is taken from an inside room to the outside ,where the air temperature is 5° F. After 1 minute the thermometer reads 55° F, and after 5minutes it reads 30° F, what is the initial temperature of the inside room? 3. A small metal bar, whose initial temperature was 20° C, is dropped into a large container of bowling water. How long will it take the bar to reach 90°C ifit is known that its temperature increase to 22°C in 1 second?4. A tank initially holds 80 gal of a brine solution containing 1/8 Ib of salt per gallon. At t = 0, another brine solution containing 1 lb of salt per gallon ispoured into the tank at the rate of 4 gal/min, while the well-stirred mixture leaves the tank at the rate of 8 gal/min. Find the amount of salt in the tankwhen the tank contains exactly 40 gal of solution

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1. A certain radioactive material follows the law of exponential growth. If between noon and 2 pm the population triples, at what time should the population become 100 times what it was at noon? 2. A thermometer is taken from an inside room to the outside ,where the air temperature is 5° F. After 1 minute the thermometer reads 55° F, and after 5 minutes it reads 30° F, what is the initial temperature of the inside room?

1. A certain radioactive material follows the law of exponential growth. If between noon and 2 pm the population triples, at what time should the population become 100 times what it was at noon? 2. A thermometer is taken from an inside room to the outside ,where the air temperature is 5° F. After 1 minute the thermometer reads 55° F, and after 5 minutes it reads 30° F, what is the initial temperature of the inside room?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Applications of differential equations

1. A certain radioactive material follows the law of exponential growth. If between noon and 2 pm the population triples, at what time should the
population become 100 times what it was at noon?
2. A thermometer is taken from an inside room to the outside ,where the air temperature is 5° F. After 1 minute the thermometer reads 55° F, and after 5
minutes it reads 30° F, what is the initial temperature of the inside room?

3. A small metal bar, whose initial temperature was 20° C, is dropped into a large container of bowling water. How long will it take the bar to reach 90°C if
it is known that its temperature increase to 22°C in 1 second?
4. A tank initially holds 80 gal of a brine solution containing 1/8 Ib of salt per gallon. At t = 0, another brine solution containing 1 lb of salt per gallon is
poured into the tank at the rate of 4 gal/min, while the well-stirred mixture leaves the tank at the rate of 8 gal/min. Find the amount of salt in the tank
when the tank contains exactly 40 gal of solution

With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.

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