
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.

Want to see the full answer?
Check out a sample textbook solution
Chapter 6 Solutions
Single Variable Calculus
- 2. Find a matrix A with the following qualities a. A is 3 x 3. b. The matrix A is not lower triangular and is not upper triangular. c. At least one value in each row is not a 1, 2,-1, -2, or 0 d. A is invertible.arrow_forwardFind the exact area inside r=2sin(2\theta ) and outside r=\sqrt(3)arrow_forwardA 20 foot ladder rests on level ground; its head (top) is against a vertical wall. The bottom of the ladder begins by being 12 feet from the wall but begins moving away at the rate of 0.1 feet per second. At what rate is the top of the ladder slipping down the wall? You may use a calculator.arrow_forward
- Explain the key points and reasons for the establishment of 12.3.2(integral Test)arrow_forwardUse 12.4.2 to determine whether the infinite series on the right side of equation 12.6.5, 12.6.6 and 12.6.7 converges for every real number x.arrow_forwarduse Cauchy Mean-Value Theorem to derive Corollary 12.6.2, and then derive 12.6.3arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning


