Suppose the cost of an object appreciates at a rate inversely proportional to the sum of its squared cost and 300. The object cost $240 when first purchased, but is worth $45 more after one year. Answer the following. 6) Write a differential equation that models this situation. Let c represent the cost (in dollars) of the object and t represent the time (in years). 7) Solve for the general solution (do not solve for c). 8) Use the initial condition to find the constant of integration, then write the particular solution (do not solve for c). 9) Use the second condition to find the constant of proportion. 10) Find the appreciation rate at t = 1 year. Round your answer to the nearest cent.

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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Suppose the cost of an object appreciates at a rate inversely proportional to the sum of its squared cost
and 300. The object cost $240 when first purchased, but is worth $45 more after one year. Answer the
following.
6) Write a differential equation that models this situation. Let c represent the cost (in dollars) of the object
and t represent the time (in years).
7) Solve for the general solution (do not solve for c).
8) Use the initial condition to find the constant of integration, then write the particular solution (do not solve
for c).
9) Use the second condition to find the constant of proportion.
10) Find the appreciation rate at t = 1 year. Round your answer to the nearest cent.
Transcribed Image Text:Suppose the cost of an object appreciates at a rate inversely proportional to the sum of its squared cost and 300. The object cost $240 when first purchased, but is worth $45 more after one year. Answer the following. 6) Write a differential equation that models this situation. Let c represent the cost (in dollars) of the object and t represent the time (in years). 7) Solve for the general solution (do not solve for c). 8) Use the initial condition to find the constant of integration, then write the particular solution (do not solve for c). 9) Use the second condition to find the constant of proportion. 10) Find the appreciation rate at t = 1 year. Round your answer to the nearest cent.
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