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?

Q: If the growth rate of the number of bacteria at any time t is proportional to the number present at…

A: Here we have to find the no of bacteria expected after two weeks.

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Q: Assume that in a certain country, the rate at which jobs are created is proportional to the number…

A: Explanation: Suppose that number of jobs  = N Here given that, the rate at which jobs are created is…

Q: Newton's law of cooling states that the temperature of an object changes at a rate proportional to…

A:

Q: Initially, 10 grams of a radioactive substance were found in a sample. It was observed In z that 20%…

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Q: A certain radioactive substance has a half-life of 38 hours. The rate of change in the decay is…

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Q: model a population p if its rate of growth is proportional to the amount present at time t

A: model a population p if its rate of growth is proportional to the amount present at time t

Q: A certain population of bacteria grows at a rate that is proportional to the number present. It is…

A: Given that: Growth rate of bacteria ∝ Number of bacteria presentNumber doubles in 2 hr

Q: Bacteria is being cultured in an agar plate. It was observed that the growth of bacteria is…

A: We will find out the required time.

Q: Consider the constant rate of depreciation value of a certain car. You bought a car amounting to 1.5…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.