Solution Found!
Applications and ExamplesThe incidence of a disease
Chapter 7, Problem 31E(choose chapter or problem)
Problem 31E
Applications and Examples
The incidence of a disease (Continuation of Example 3.) Suppose that in any given year the number of cases can be reduced by 25% instead of 20%.
a. How long will it take to reduce the number of cases to 1000?
b. How long will it take to eradicate the disease, that is, reduce the number of cases to less than 1?
Reference: Example 3
One model for the way diseases die out when properly treated assumes that the rate dy/ dt at which the number of infected people changes is proportional to the number y. The number of people cured is proportional to the number y that are infected with the disease. Suppose that in the course of any given year the number of cases of a disease is reduced by 20%. If there are 10,000 cases today, how many years will it take to reduce the number to 1000?
Questions & Answers
QUESTION:
Problem 31E
Applications and Examples
The incidence of a disease (Continuation of Example 3.) Suppose that in any given year the number of cases can be reduced by 25% instead of 20%.
a. How long will it take to reduce the number of cases to 1000?
b. How long will it take to eradicate the disease, that is, reduce the number of cases to less than 1?
Reference: Example 3
One model for the way diseases die out when properly treated assumes that the rate dy/ dt at which the number of infected people changes is proportional to the number y. The number of people cured is proportional to the number y that are infected with the disease. Suppose that in the course of any given year the number of cases of a disease is reduced by 20%. If there are 10,000 cases today, how many years will it take to reduce the number to 1000?
ANSWER:
Solution:
Step 1 of 5:
a)In this problem, we need to find if there are 10,000 cases today, how many years will it take to reduce the number to 1000.