An insurance company is setting up a way to evaluate the monthly premium of a medical insurance for doctors. To obtain a more accurate model, they want to set it up as a differential equation with: Output: I = the price of the medical insurance in Canadian dollars Input: y = the number of years a doctor has been in service Their model must satisfy the following requirements: The price I should increase proportionally to the number of misdiagnoses M and inversely proportionally to the doctor's experience with one proportionality constant for both; The number of misdiagnoses Mis modelled by the square root of the years the doctor has been in service; A doctor's experience E is given by the difference between the square of the years the doctor has been in service and the number of missed diagnoses; When a doctor reaches 4 misdiagnoses, then the insurance price should be set as CAD$ 1890. To help the insurance company, set up a differential equation that satisfies the requirements above: dy Hint: Your answer should depend only on y and I. insurance company people know enough about differential equations to understand that a differential equation has infinitely many solutions, so they also need you to give them an "initial condition": 10
An insurance company is setting up a way to evaluate the monthly premium of a medical insurance for doctors. To obtain a more accurate model, they want to set it up as a differential equation with: Output: I = the price of the medical insurance in Canadian dollars Input: y = the number of years a doctor has been in service Their model must satisfy the following requirements: The price I should increase proportionally to the number of misdiagnoses M and inversely proportionally to the doctor's experience with one proportionality constant for both; The number of misdiagnoses Mis modelled by the square root of the years the doctor has been in service; A doctor's experience E is given by the difference between the square of the years the doctor has been in service and the number of missed diagnoses; When a doctor reaches 4 misdiagnoses, then the insurance price should be set as CAD$ 1890. To help the insurance company, set up a differential equation that satisfies the requirements above: dy Hint: Your answer should depend only on y and I. insurance company people know enough about differential equations to understand that a differential equation has infinitely many solutions, so they also need you to give them an "initial condition": 10
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:An insurance company is setting up a way to evaluate the monthly premium of a medical insurance for doctors.
To obtain a more accurate model, they want to set it up as a differential equation with:
• Output: I = the price of the medical insurance in Canadian dollars
• Input y = the number of years a doctor has been in service
Their model must satisfy the following requirements:
1. The price I should increase proportionally to the number of misdiagnoses M and inversely proportionally to the doctor's experience - with one
proportionality constant for both;
2. The number of misdiagnoses M is modelled by the square root of the years the doctor has been in service;
3. A doctor's experience is given by the difference between the square of the years the doctor has been in service and the number of missed
diagnoses;
4. When a doctor reaches 4 misdiagnoses, then the insurance price should be set as CAD$ 1890.
To help the insurance company, set up a differential equation that satisfies the requirements above:
dI
dy
Hint: Your answer should depend only on y and I.
The insurance company people know enough about differential equations to understand that a differential equation has infinitely many solutions, so they
also need you to give them an "initial condition":
¹0-0
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