Assignment:
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.
Provide complete and step by step solution for the question and show calculations and use formulas.