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All Differential Equations Resources

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Flashcards: Mathematical Models

Suppose a dog is carrying a virus returns to a isolated doggy day care of 40 dogs. Determine the differential equation for the number of dogs D(t) who have contracted the virus if the rate at which it spreads is proportional to the number of interactions between the dogs with the virus and the dogs that have not yet come in contact with the virus.

$\frac{dD}{dt}=kP$

$\frac{dD}{dt}=kD(40-D)$

$\frac{dD}{dt}=k(40-D)$

$\frac{dD}{dt}=k40-D^2$

$\frac{dD}{dt}=kD$

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Flashcards: Mathematical Models

Your answer:

$\frac{dD}{dt}=kP$

Your answer:

$\frac{dD}{dt}=k(40-D)$

Your answer:

$\frac{dD}{dt}=k40-D^2$

Your answer:

$\frac{dD}{dt}=kD$

Correct answer:

$\frac{dD}{dt}=kD(40-D)$

Explanation:

This question is asking a population dynamic type of scenario.

The total population in terms of time and where is the constant rate of proportionality, is described by the following differential equation.

$\frac{dP}{dt}=kP$

For this particular function it's known that the population is in the form to represent the dogs. Since the virus spreads based on the interactions between the dogs who have the virus and those who have not yet contracted it, the population will be the product of the number of dogs with the virus and those without the virus.

Therefore the differential equation becomes,

$\frac{dD}{dt}=kD(40-D)$

Flashcards: Mathematical Models

$\frac{dD}{dt}=kP$

$\frac{dD}{dt}=k(40-D)$

$\frac{dD}{dt}=kD(40-D)$

$\frac{dD}{dt}=kD$

$\frac{dD}{dt}=k40-D^2$

Report an Error Copyright Notice

Flashcards: Mathematical Models

Your answer:

$\frac{dD}{dt}=kP$

Your answer:

$\frac{dD}{dt}=k(40-D)$

Your answer:

$\frac{dD}{dt}=kD$

Your answer:

$\frac{dD}{dt}=k40-D^2$

Correct answer:

$\frac{dD}{dt}=kD(40-D)$

Explanation:

This question is asking a population dynamic type of scenario.

The total population in terms of time and where is the constant rate of proportionality, is described by the following differential equation.

$\frac{dP}{dt}=kP$

Therefore the differential equation becomes,

$\frac{dD}{dt}=kD(40-D)$

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All Differential Equations Resources

Flashcards: Mathematical Models

Flashcards: Mathematical Models

Flashcards: Mathematical Models

Flashcards: Mathematical Models

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All Differential Equations Resources

Flashcards: Mathematical Models

Flashcards: Mathematical Models

Flashcards: Mathematical Models

Flashcards: Mathematical Models

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

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