   Chapter 1.4, Problem 32E ### 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

# An isotope of sodium, 24Na, has a half-life of 15 hours. A sample of this isotope has mass 2 g.(a) Find the amount remaining after 60 hours.(b) Find the amount remaining after t hours.(c) Estimate the amount remaining after 4 days.(d) Use a graph to estimate the time required for the mass to he reduced to 0.01 g.

(a)

To determine

To find: The amount remaining isotope of sodium after 60 hours.

Explanation

Given:

The half-life of sodium is 15 hours.

The mass of sample sodium = 2g.

Calculation:

Let m0 be the initial mass of sodium.

That is m0=2g .

After 15 hours the amount of sodium is m1=12m0 .

Substitute 2g for m0 in m1 ,

m1=12(2)m1=1g

After 30 hours the amount of sodium m2=12m1

Substitute 1g for m1 in m2 ,

m2=12(1)m2=0

(b)

To determine

To find: The amount of sodium after t hours.

(c)

To determine

To estimate: The remaining amount of sodium after 4 days.

(d)

To determine

To estimate: The amount of bismuth reduced to 0.01g.

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