17. A pond initially contains 1,000,000 gal of water and an unknown amount of an undesirable chemical. Water containing 0.01 grams of this chemical per gallon flows into the pond at a rate of 300 gal/h. The mixture flows out at the same rate, so the amount of water in the pond remains constant. Assume that the chemical is uniformly distributed throughout the pond. a. Write a differential equation for the amount of chemical in the pond at any time. b. How much of the chemical will be in the pond after a very long time? Does this limiting amount depend on the amount that was present initially? c. Write a differential equation for the concentration of the chemical in the pond at time t. Hint: The concentration is c = a/v = a(t)/ 106.
17. A pond initially contains 1,000,000 gal of water and an unknown amount of an undesirable chemical. Water containing 0.01 grams of this chemical per gallon flows into the pond at a rate of 300 gal/h. The mixture flows out at the same rate, so the amount of water in the pond remains constant. Assume that the chemical is uniformly distributed throughout the pond. a. Write a differential equation for the amount of chemical in the pond at any time. b. How much of the chemical will be in the pond after a very long time? Does this limiting amount depend on the amount that was present initially? c. Write a differential equation for the concentration of the chemical in the pond at time t. Hint: The concentration is c = a/v = a(t)/ 106.
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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17
Transcribed Image Text:RE 1.1.10 Problem 10
17. A pond initially contains 1,000,000 gal of water and an unknown
amount of an undesirable chemical. Water containing 0.01 grams of
this chemical per gallon flows into the pond at a rate of 300 gal/h. The
mixture flows out at the same rate, so the amount of water in the pond
remains constant. Assume that the chemical is uniformly distributed
throughout the pond.
a. Write a differential equation for the amount of chemical in
the pond at any time.
b. How much of the chemical will be in the pond after a very
long time? Does this limiting amount depend on the amount that
was present initially?
c. Write a differential equation for the concentration of the
chemical in the pond at time t. Hint: The concentration is
c = a/v = a(t)/106.
18. A spherical raindrop evaporates at a rate proportional to its
surface area. Write a differential equation for the volume of the
raindrop as a function of time.
19. Newton's law of cooling states that the temperature of an
object changes at a rate proportional to the difference between the
temperature of the object itself and the temperature of its surroundings
(the ambient air temperature in most cases). Suppose that the ambient
temperature is 70°F and that the rate constant is 0.05 (min)-¹. Write a
differential equation for the temperature of the object at any time. Note
that the differential equation is the same whether the temperature of
the object is above or below the ambient temperature.
1.2
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Solutions of Some Differentia
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