Show that the solution N of the exponential decay equation NP -kN and initial condition 1 dt N(0) = N, is N(t) = N,e* 2 A radioactive material constant k and half-life 7, are related by the equation kì = In 2, and that the half-life of a radioactive substance is the time À such that N(X) =-N(0)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 9T
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Show that the
dN
= -kN and initial condition
dt
1
solution N of the exponential decay equation
N(0) = N, is N(t) = N„e
2
A radioactive material constant k and half-life i, are related by the equation
k就= In2,
and that the half-life of a radioactive substance is the time î such that
N(3) = -N(0)
Transcribed Image Text:Show that the dN = -kN and initial condition dt 1 solution N of the exponential decay equation N(0) = N, is N(t) = N„e 2 A radioactive material constant k and half-life i, are related by the equation k就= In2, and that the half-life of a radioactive substance is the time î such that N(3) = -N(0)
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