Suppose That an Epidemic Is Spreading at a Rate Proportional $y ^ { \prime } = g ( y )$

question 126

Multiple Choice

Suppose that an epidemic is spreading at a rate proportional to the square of the infected population. Let f(t) be the number of infected people at time t, and suppose y = f(t) satisfies a differential equation $y ^ { \prime } = g ( y )$ . Which of the following sets of curves could represent solutions of $y ^ { \prime } = g ( y ) ?$ [Hint: First determine the differential equation $y ^ { \prime }$ = g(y) .]

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Definitions:

Absorption

The process by which substances are taken up and assimilated into the body, such as nutrients from food or drugs into the bloodstream.

Binge-Eating Disorder

A serious eating disorder characterized by recurrent episodes of eating large quantities of food, often quickly and to the point of discomfort.

Anorexia Nervosa

An eating disorder characterized by an obsessive fear of gaining weight, leading to severe restrictions on food intake and body weight loss.

Bulimia Nervosa

An eating disorder characterized by binge eating followed by purging, such as vomiting or using laxatives, to prevent weight gain.