Suppose an Infectious Disease Spreads Through an Elementary School at a Rate

question 118

True/False

Suppose an infectious disease spreads through an elementary school at a rate proportional to the product of the percentage of pupils who have the disease and the percentage of pupils who have not yet contracted the disease. Suppose that at the beginning of the epidemic 5% of the pupils have the disease. Let f(t) be the percentage of pupils who have the disease at time t; give the differential equation satisfied by f(t). Does the following accurately describe this situation: $y ^ { \prime }$ = ky(100 - y); y(0) = 0.05, where k is a positive constant?

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Definitions:

Antibiotic Medium

A growth medium infused with antibiotics used in laboratory settings to select for or against microorganisms sensitive to the specific antibiotics.

Human DNA Fragments

Short sequences or pieces of human deoxyribonucleic acid (DNA) that result from breaking the molecule into smaller components.

Plasmids

Small, circular, double-stranded DNA molecules found in bacteria and some other organisms, capable of independent replication and often used in genetic engineering.

Polymerase Chain Reaction

A laboratory technique used to amplify DNA sequences, making millions of copies of a specific DNA segment.