We showed by Formula (19) of Section 8.2 that if there arey0 units of radioactive
Chapter 9, Problem 41(choose chapter or problem)
We showed by Formula (19) of Section that if there are \(y_{0}\) units of radioactive carbon- 14 present at time \(t=0\), then the number of units present \(t\) years later is
\(y(t)=y_{0} e^{-0.000121 t}\)
(a) Express \(y^{(t)}\) as a Maclaurin series.
(b) Use the first two terms in the series to show that the number of units present after 1 year is
approximately \((0.999879) y_{0}\)
(c) Compare this to the value produced by the formula for \(y^{(t)}\)
Equation Transcription:
Text Transcription:
Y_0
t=0
y(t)=y_0 e^-0.000121t
y(t)
(0.999879)y_0
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