   Chapter 2.3, Problem 49E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

Half-Life The amount of radium 226 remaining in a sample that originally contained A grams is approximately C ( t ) = A ( 0.999567 ) t , where t is time in years. Find the half-life to the nearest 100 years. [HINT: See Example 3a.]

To determine

To calculate: The half life time of the radium 226 sample if the remaining amount of radium 226 that is C(t) in a sample is given be the expression, C(t)=A(0.999567)t.

Explanation

Given Information:

The remaining amount of radium 226 in a sample is given be the expression,

C(t)=A(0.999567)t

Here, C(t) is remaining amount of radium 226, A is initial amount of the radium 226 and t is the time in year.

Formula used:

The logarithmic relation for indices is,

logbx=xlogb

Calculation:

Consider the expression of remaining amount of radium 226 in a sample,

C(t)=A(0.999567)t

At the half-life time, the final amount would be half of the initial amount of the radium 226.

Therefore,

c(t)=0.5A

Substitute c(t)=0.5A in the formula C(t)=A(0.999567)t,

0.5A=A(0.999567)t

Divide both side by A,

0

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