   Chapter 3.8, Problem 10E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# A sample oflritium-3 decayed to 94.5% of its original amount after a year.(a) What is the half-life of lritium-3?(b) How long would it take the sample to decay to 20% of its original amount?

(a)

To determine

To find: The half-life of tritium-3.

Explanation

Given:

Let N(t) be the amount of sample of tritium-3 after t years.

N(1)=0.945 and N0=1.

Theorem used:

“The only solutions of the differential equation dydt=ky are the exponential functions

y(t)=y(0)ekt.”

Calculation:

By using theorem as stated above,

N(t)=N0ekt (1)

Substitute N(t)=0.945,t=1 and N0=1 in equation (1),

0.945=1ek0.945=ek

Take natural logarithm on both sides,

ln0.945=lnekln0.945=k

Substitute ln0.945=k in equation (1),

N(t)=eln0.945tN(t)=(eln0

(b)

To determine

To find: The time that take the sample to decay to 20% of its original amount.

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