Concept explainers
(a)
To express: The amount of substance remaining as a function of time.
(a)
Answer to Problem 46E
The amount of substance remaining as a function of time is
Explanation of Solution
Given information: The half-life of substance is
Calculation:
The formula of exponential growth is
Here,
So,
The amount of substance remaining as a function of time can be expressed as follows:
Therefore, the amount of substance remaining as a function of time can be expressed as
(b)
To find: The required time such that substance remains 1 gram.
(b)
Answer to Problem 46E
The substance will remain 1 gram after
Explanation of Solution
Given information: The half-life of substance is
Calculation:
Consider the function
Substitute 1 for
Simplify further.
Therefore, the substance will remain 1 gram after
Chapter 1 Solutions
Calculus: Graphical, Numerical, Algebraic: Solutions Manual
Additional Math Textbook Solutions
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University Calculus: Early Transcendentals (3rd Edition)
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