# Modeling using Differential Equations

One model for the spread of a rumor is that the rate of spread is proportional to the product of the fraction y of the population who have heard the rumor and the fraction who have not heard the rumor:

a) Write a differential equation that is satisfied by y ( use k for the constant of proportionality)

dy/dt =

b) Solve the differential equation

assume y(0) = 0

y =

c )A small town has 1100 inhabitants . At 8am , 100 people have heard a rumor. By noon half the town has heard it. At what time will 90% of the population have heard the rumor (round to one decimal place).

Hours after the beginning = have a real block with this type of questions.

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#### Solution Summary

Differential equations are solved.

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