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The Extrasoft Toy Co. has just released its latest creation, a plush platypus named "Eggbert." The demand function for Eggbert dolls is D(p) = 52,000 - 500p dolls per month when the price is p dollars. The supply function is S(p) = 31,000 + 500p dolls per month when the price is p dollars. This makes the equilibrium price $21. The Evans price adjustment model assumes that if the price is set at a value other than the equilibrium price, it will change over time in such a way that its rate of change is proportional to the shortage D(p) - S(p). (a) Write the differential equation given by the Evans price adjustment model for the price p as a function of time. (Use k for the constant of proportionality.) dp dt (b) Find the general solution of the differential equation you wrote in part (a). (You will have two unknown constants, one being the constant of proportionality.) p(t) = (c) Find the particular solution in which Eggbert dolls are initially priced at $10 and the price rises to $12 after one month (t = 1). p(t) =

The Extrasoft Toy Co. has just released its latest creation, a plush platypus named "Eggbert." The demand function for Eggbert dolls is D(p) = 52,000 - 500p dolls per month when the price is p dollars. The supply function is S(p) = 31,000 + 500p dolls per month when the price is p dollars. This makes the equilibrium price $21. The Evans price adjustment model assumes that if the price is set at a value other than the equilibrium price, it will change over time in such a way that its rate of change is proportional to the shortage D(p) - S(p). (a) Write the differential equation given by the Evans price adjustment model for the price p as a function of time. (Use k for the constant of proportionality.) dp dt (b) Find the general solution of the differential equation you wrote in part (a). (You will have two unknown constants, one being the constant of proportionality.) p(t) = (c) Find the particular solution in which Eggbert dolls are initially priced at $10 and the price rises to $12 after one month (t = 1). p(t) =

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...
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The Extrasoft Toy Co. has just released its latest creation, a plush platypus named "Eggbert." The demand function for Eggbert dolls is D(p) = 52,000 – 500p dolls per month when the price is p dollars. The supply function is S(p) = 31,000 + 500p dolls per month when the price is p dollars. This makes the equilibrium price $21. The Evans price adjustment model assumes that if the price is set at a value other than the equilibrium price, it will change over time in such a way that its rate of change is proportional to the shortage D(p) – S(p). (a) Write the differential equation given by the Evans price adjustment model for the price p as a function of time. (Use k for the constant of proportionality.) dp dt (b) Find the general solution of the differential equation you wrote in part (a). (You will have two unknown constants, one being the constant of proportionality.) p(t) = (c) Find the particular solution in which Eggbert dolls are initially priced at $10 and the price rises to $12 after one month (t = 1). p(t) =
Transcribed Image Text:The Extrasoft Toy Co. has just released its latest creation, a plush platypus named "Eggbert." The demand function for Eggbert dolls is D(p) = 52,000 – 500p dolls per month when the price is p dollars. The supply function is S(p) = 31,000 + 500p dolls per month when the price is p dollars. This makes the equilibrium price $21. The Evans price adjustment model assumes that if the price is set at a value other than the equilibrium price, it will change over time in such a way that its rate of change is proportional to the shortage D(p) – S(p). (a) Write the differential equation given by the Evans price adjustment model for the price p as a function of time. (Use k for the constant of proportionality.) dp dt (b) Find the general solution of the differential equation you wrote in part (a). (You will have two unknown constants, one being the constant of proportionality.) p(t) = (c) Find the particular solution in which Eggbert dolls are initially priced at $10 and the price rises to $12 after one month (t = 1). p(t) =
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