years. When air is released from an inflated balloon it is found that the rate of decrease of the volume of the balloon is proportional to the volume of the balloon. This can be represented by the -kv, where v is the volume, t is the time and k is the constant of dy differential equation dr proportionality. (a) If the initial volume of the balloon is vo, find an expression, in terms of k, for the volume of the balloon at time 1. Vo (b) Find an expression, in terms of k, for the time when the volume is

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.6: Variation
Problem 2E
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years.
4. When air is released from an inflated balloon it is found that the rate of decrease of the volume
of the balloon is proportional to the volume of the balloon. This can be represented by the
differential equation
dy
dt
kv, where v is the volume, t is the time and k is the constant of
proportionality.
(a) If the initial volume of the balloon is vo, find an expression, in terms of k, for the volume
of the balloon at time 1.
Vo
(b) Find an expression, in terms of k, for the time when the volume is
2
Transcribed Image Text:years. 4. When air is released from an inflated balloon it is found that the rate of decrease of the volume of the balloon is proportional to the volume of the balloon. This can be represented by the differential equation dy dt kv, where v is the volume, t is the time and k is the constant of proportionality. (a) If the initial volume of the balloon is vo, find an expression, in terms of k, for the volume of the balloon at time 1. Vo (b) Find an expression, in terms of k, for the time when the volume is 2
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