The amount of a radioactive substance, y, decays exponentially such that its half-life is 8 days. In other words, the amount of any sample decays to exactly half in that time period. Write a differential equation in terms of y and t, in days, to represent the rate of decrease in the amount of the substance. dy dt dy = 0.1732y dt dy dt = -0.0433y dy dt = -0.1732y : -0.0866y

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
The amount of a radioactive substance, y, decays exponentially such that its half-life is 8 days. In other words, the amount of any
sample decays to exactly half in that time period.
Write a differential equation in terms of y and t, in days, to represent the rate of decrease in the amount of the substance.
O
dy = -0.0433y
| |
dt
dy
dt
0.1732y
= -0.1732y
dy = -0.0866y
dt
Transcribed Image Text:The amount of a radioactive substance, y, decays exponentially such that its half-life is 8 days. In other words, the amount of any sample decays to exactly half in that time period. Write a differential equation in terms of y and t, in days, to represent the rate of decrease in the amount of the substance. O dy = -0.0433y | | dt dy dt 0.1732y = -0.1732y dy = -0.0866y dt
Expert Solution
steps

Step by step

Solved in 2 steps

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