A radioactive substance decays at a rate proportional to its mass. A particular specimen of the substance is found to have a mass of 25 grams and is decaying at a rate of 0.025 grams per year. There are m grams left after t years. dm (a) Show that a differential equation relating m and t is =-0.001m dt (b) Find the mass of the specimen after 10 years. c) Find how long it will take for the specimen to decay to 5 grams.

A radioactive substance decays at a rate proportional to its mass. A particular specimen of the substance is found to have a mass of 25 grams and is decaying at a rate of 0.025 grams per year. There are m grams left after t years. dm (a) Show that a differential equation relating m and t is =-0.001m dt (b) Find the mass of the specimen after 10 years. c) Find how long it will take for the specimen to decay to 5 grams.

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...

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

A radioactive substance decays at a rate proportional to its mass. A particular specimen of the
substance is found to have a mass of 25 grams and is decaying at a rate of 0.025 grams per year.
There are m grams left after t years.
dm
(a) Show that a differential equation relating m and t is =-0.001m
dt
(b) Find the mass of the specimen after 10 years.
c) Find how long it will take for the specimen to decay to 5 grams.

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