Homework Help is Here – Start Your Trial Now!
Math
Calculus
b) Solve the differential equation found in a) to derive the general equation that describes the amount of y present at time t for exponential growth or decay. c) In problem b) the solution should be: y = y,e where yo is the original amount at t = 0, and k > 0 is growth, k < 0 is decay, and k is the rate of growth (or decay). Now answer the following from the perspective of the differential equation found in a): i) Why is yo called the original amount? ii) Why is it called growth when k > 0? i) Why is it called decay when k < 0? iv) Why is it k called the growth/decay rate? v) Why is k also called the constant of proportionality?

b) Solve the differential equation found in a) to derive the general equation that describes the amount of y present at time t for exponential growth or decay. c) In problem b) the solution should be: y = y,e where yo is the original amount at t = 0, and k > 0 is growth, k < 0 is decay, and k is the rate of growth (or decay). Now answer the following from the perspective of the differential equation found in a): i) Why is yo called the original amount? ii) Why is it called growth when k > 0? i) Why is it called decay when k < 0? iv) Why is it k called the growth/decay rate? v) Why is k also called the constant of proportionality?

Calculus: Early Transcendentals
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...
See similar textbooks
icon
Related questions
Question
100%
3) The general equation for exponential growth and decay is derived from the differential equation described with the following sentence: The rate of change of variable y is proportional to the value of y. This statement describes a differential equation. The differential equation can be solved to find the particular solution as follows: y= y,e* With (0,yo) as the initial condition given. This is called exponential growth, and the formula is commonly found in algebra 2 and precalculus textbooks. See below for example. The formula below is the solution to the differential equation that describes – the rate of change of P is proportional to P, where k is the growth/decay rate, and the initial amount is Po
Transcribed Image Text:3) The general equation for exponential growth and decay is derived from the differential equation described with the following sentence: The rate of change of variable y is proportional to the value of y. This statement describes a differential equation. The differential equation can be solved to find the particular solution as follows: y= y,e* With (0,yo) as the initial condition given. This is called exponential growth, and the formula is commonly found in algebra 2 and precalculus textbooks. See below for example. The formula below is the solution to the differential equation that describes – the rate of change of P is proportional to P, where k is the growth/decay rate, and the initial amount is Po
b) Solve the differential equation found in a) to derive the general equation that describes the amount of y present at time t for exponential growth or decay. c) In problem b) the solution should be: y= y,e* where yo is the original amount at t = 0, and k >0 is growth, k< 0 is decay, and k is the rate of growth (or decay). Now answer the following from the perspective of the differential equation found in a): i) Why is yo called the original amount? ii) Why is it called growth when k > 0? iii) Why is it called decay when k< 0? iv) Why is it k called the growth/decay rate? v) Why is k also called the constant of proportionality?
Transcribed Image Text:b) Solve the differential equation found in a) to derive the general equation that describes the amount of y present at time t for exponential growth or decay. c) In problem b) the solution should be: y= y,e* where yo is the original amount at t = 0, and k >0 is growth, k< 0 is decay, and k is the rate of growth (or decay). Now answer the following from the perspective of the differential equation found in a): i) Why is yo called the original amount? ii) Why is it called growth when k > 0? iii) Why is it called decay when k< 0? iv) Why is it k called the growth/decay rate? v) Why is k also called the constant of proportionality?
Expert Solution
steps

Step by step

Solved in 4 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Differential Equation
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
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
SEE MORE TEXTBOOKS