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)

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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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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