(a.)
The amount of substance remaining as a function of time
(a.)
Answer to Problem 46E
It has been determined that the amount of substance remaining as a function of time
Explanation of Solution
Given:
The half-life of a certain radioactive substance is
Concept used:
The differential equation that models radioactive decay is given as
Calculation:
As discussed, the equation for radioactive decay is,
Simplifying,
Now, it is given that there are
Then,
It is also given that the half-life of the radioactive substance is
Then,
Integrating both sides of
Solving,
On further solving,
Simplifying,
On further simplifying,
Continuing simplification,
Finally,
Put
Integrating both sides with appropriate limits, assuming that
Solving,
On further solving,
Simplifying,
On further simplifying,
Finally,
This is the required expression for the amount of substance remaining as a function of time
Conclusion:
It has been determined that the amount of substance remaining as a function of time
(b.)
The time when there will be
(b.)
Answer to Problem 46E
It has been determined that there will be
Explanation of Solution
Given:
The half-life of a certain radioactive substance is
Concept used:
The differential equation that models radioactive decay is given as
Calculation:
As determined previously, the amount of substance remaining as a function of time
Note that, here, the unit of
Now, according to the problem,
Put
Simplifying,
On further simplification,
Continuing simplification,
This implies that there will be
Conclusion:
It has been determined that there will be
Chapter 0 Solutions
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