Concept explainers
Under certain circumstances a rumor spreads according to the equation
where p(t) is the proportion of the population that has heard the rumor at time t and a and k are positive constants. [In Section 9.4 we will see that this is a reasonable equation for p(t).]
(a) Find limt→∞ p(t).
(b) Find the rate of spread of the rumor.
(c) Graph p for the case a = 10, k = 0.5 with t measured in hours. Use the graph to estimate how long it will take for 80% of the population to hear the rumor.
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Single Variable Calculus
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