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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 = k[21000 – 1000p] 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.) cal p(t) = Ope Fur (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). Syr Rel 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 = k[21000 – 1000p] 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.) cal p(t) = Ope Fur (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). Syr Rel 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 answer is NOT, I put those answers in and it said they were wrong for parts b and c.

b) 21-Ae^{-kt}

c) 21-11e^{0.2006t}

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 |시21000-1000p] 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.) cal p(t) = Op Fur (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). Syr Rel p(t) = Set Vec
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 |시21000-1000p] 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.) cal p(t) = Op Fur (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). Syr Rel p(t) = Set Vec
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