62. We may use a recursively defined sequence to ap- proximate the current amount of a radioactive ele- ment. For example, radioactive radium changes into lead over time. The rate of decay is proportional to the amount of radium present. Experimental data sug- gests that a gram of radium decays into lead at a rate of gram per year. Let a; be the amount of radium 2337 at the end of year k. Since the decay rate is constant, if we use a linear model to approximate the amount that remains after one year has passes, we have 2336 ao. 2337 1 a1 = ao - 2337 ao More generally, we obtain the recursion formula 2336 ak+1 2337 Use this formula to estimate how much radium remains after 100 years if we start off with ao radium. 10 grams of
62. We may use a recursively defined sequence to ap- proximate the current amount of a radioactive ele- ment. For example, radioactive radium changes into lead over time. The rate of decay is proportional to the amount of radium present. Experimental data sug- gests that a gram of radium decays into lead at a rate of gram per year. Let a; be the amount of radium 2337 at the end of year k. Since the decay rate is constant, if we use a linear model to approximate the amount that remains after one year has passes, we have 2336 ao. 2337 1 a1 = ao - 2337 ao More generally, we obtain the recursion formula 2336 ak+1 2337 Use this formula to estimate how much radium remains after 100 years if we start off with ao radium. 10 grams of
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 81E
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Transcribed Image Text:62. We may use a recursively defined sequence to ap-
proximate the current amount of a radioactive ele-
ment. For example, radioactive radium changes into
lead over time. The rate of decay is proportional to the
amount of radium present. Experimental data sug-
gests that a gram of radium decays into lead at a rate
of
gram per year. Let a; be the amount of radium
2337
at the end of year k. Since the decay rate is constant,
if we use a linear model to approximate the amount
that remains after one year has passes, we have
2336
ao.
2337
1
a1 = ao -
2337
ao
More generally, we obtain the recursion formula
2336
ak+1
2337
Use this formula to estimate how much radium remains
after 100 years if we start off with ao
radium.
10 grams of
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