Rate of Evaporation The Los Angeles Zoo plans to transport a California sea lion to the San Diego Zoo. The animal will be wrapped in a wet blanket during the trip. At any time t, the blanket will lose water (due to evaporation) at a rate proportional to the amount f(t) of water in the blanket, with constant of proportionality k = -.3. Initially, the blanket will contain 2 gallons of seawater. (a) Set up the differential equation satisfied by f(t). (b) Use Euler's method with n = 2 to estimate the amount of %3D moisture in the blanket after 1 hour. (c) Solve the differential equation in part (a) and compute f(1). (d) Compare the answers in parts (b) and (c) and approxi- mate the error in using Euler's method.
Rate of Evaporation The Los Angeles Zoo plans to transport a California sea lion to the San Diego Zoo. The animal will be wrapped in a wet blanket during the trip. At any time t, the blanket will lose water (due to evaporation) at a rate proportional to the amount f(t) of water in the blanket, with constant of proportionality k = -.3. Initially, the blanket will contain 2 gallons of seawater. (a) Set up the differential equation satisfied by f(t). (b) Use Euler's method with n = 2 to estimate the amount of %3D moisture in the blanket after 1 hour. (c) Solve the differential equation in part (a) and compute f(1). (d) Compare the answers in parts (b) and (c) and approxi- mate the error in using Euler's method.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:Rate of Evaporation The Los Angeles Zoo plans to transport
a California sea lion to the San Diego Zoo. The animal will
be wrapped in a wet blanket during the trip. At any time
t, the blanket will lose water (due to evaporation) at a rate
Transcribed Image Text:proportional to the amount f(t) of water in the blanket, with
constant of proportionality k = -.3. Initially, the blanket will
contain 2 gallons of seawater.
(a) Set up the differential equation satisfied by f(t).
(b) Use Euler's method with n = 2 to estimate the amount of
%3D
moisture in the blanket after 1 hour.
(c) Solve the differential equation in part (a) and compute f(1).
(d) Compare the answers in parts (b) and (c) and approxi-
mate the error in using Euler's method.
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