7. A radioactive isotope decays at a rate y'(t) = -ky(t) proportional to the amount y(t) remaining at time t. Express the half-life of the isotope in terms of the constant k. The half-life means the time it takes for y(t) to reach one half of its initial value y(0).

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
icon
Related questions
Question

I will make sure to thumbs up !

7. A radioactive isotope decays at a rate
y'(t) = -ky(t)
proportional to the amount y(t) remaining at time t. Express the half-life of the isotope in
terms of the constant k. The half-life means the time it takes for y(t) to reach one half of
its initial value y(0).
Transcribed Image Text:7. A radioactive isotope decays at a rate y'(t) = -ky(t) proportional to the amount y(t) remaining at time t. Express the half-life of the isotope in terms of the constant k. The half-life means the time it takes for y(t) to reach one half of its initial value y(0).
Expert Solution
steps

Step by step

Solved in 4 steps with 2 images

Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning