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 model for p(t).]
(a) Find
(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.
Trending nowThis is a popular solution!
Chapter 6 Solutions
Single Variable Calculus
- bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.arrow_forwardFind derivatives of the functions defined as follows. y=-4e-0.3xarrow_forwardDoes a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it continues on its course indefinitely. Let D(t) denote its distance from Earth after t years of travel. Do you expect that D has a limiting value?arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,