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Math
CalculusSingle Variable Calculus8th Edition

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Chapter 6.2, Problem 65E
BuyFindarrow_forward

Single Variable Calculus

8th Edition
James Stewart
ISBN: 9781305266636

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
Problem 45E
Problem 46E
Problem 47E
Problem 48E
Problem 49E
Problem 50E
Problem 51E
Problem 52E
Problem 53E
Problem 54E
Problem 55E
Problem 56E
Problem 57E
Problem 58E
Problem 59E
Problem 60E
Problem 61E
Problem 62E
Problem 63E
Problem 65E
Problem 66E
Problem 67E
Problem 68E
Problem 69E
Problem 70E
Problem 71E
Problem 72E
Problem 73E
Problem 74E
Problem 75E
Problem 76E
Problem 77E
Problem 78E
Problem 79E
Problem 80E
Problem 81E
Problem 82E
Problem 83E
Problem 84E
Problem 85E
Problem 86E
Problem 87E
Problem 88E
Problem 89E
Problem 90E
Problem 91E
Problem 92E
Problem 93E
Problem 94E
Problem 95E
Problem 96E
Problem 97E
Problem 98E
Problem 99E
Problem 100E
Problem 101E
Problem 102E
Problem 103E
Problem 104E
Problem 105E
Problem 106E
Problem 107E
Problem 108E
Problem 109E
Problem 110E
Problem 111E
Problem 1AE
Problem 2AE
Problem 3AE
Problem 4AE
Problem 5AE
Problem 6AE
Problem 7AE
Problem 8AE
Problem 9AE
Problem 10AE
Problem 11AE
Problem 12AE
Problem 13AE
Problem 14AE
Problem 15AE
Problem 16AE
Problem 17AE
Problem 18AE
Problem 19AE
Problem 20AE
Problem 21AE
Problem 22AE
Problem 23AE
Problem 24AE
Problem 25AE
Problem 26AE
Problem 27AE
Problem 28AE
Problem 29AE
Problem 30AE
Problem 31AE
Problem 32AE
Problem 33AE
Problem 34AE
Problem 35AE
Problem 36AE
Problem 37AE
Problem 38AE
Problem 39AE
Problem 40AE
Problem 41AE
Problem 42AE
Problem 43AE
Problem 44AE
Problem 45AE
Problem 46AE
Problem 47AE
Problem 48AE
Problem 49AE
Problem 50AE
Problem 51AE
Problem 52AE
Problem 53AE
Problem 54AE
Problem 55AE
Problem 56AE
Problem 57AE
Problem 58AE
Problem 60AE
Problem 61AE
Problem 62AE
Problem 63AE
Problem 64AE
Problem 65AE
Problem 66AE
Problem 67AE
Problem 68AE
Problem 69AE
Problem 70AE
Problem 71AE
Problem 72AE
Problem 73AE
Problem 74AE
Problem 75AE
Problem 76AE
Problem 77AE
Problem 78AE
Problem 79AE
Problem 80AE
Problem 81AE
Problem 82AE
Problem 83AE
Problem 84AE
Problem 85AE
Problem 86AE
Problem 87AE
Problem 88AE
Problem 89AE
BuyFindarrow_forward

Single Variable Calculus

8th Edition
James Stewart
ISBN: 9781305266636
Textbook Problem

Under certain circumstances a rumor spreads according to the equation

p ( t )   =   1 1 + a e − k t

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 lim t → ∞ 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.

(a)

To determine

To find: The limit of the function limt→∞p(t).

Explanation

Obtain limit of the function.

That is, compute limt→∞p(t).

limt→∞p(t)=limt→∞(11+ae−kt)=limt→∞(11+aekt</

(b)

To determine

To find: The rate of spread of the rumor.

(c)

To determine

To sketch: The graph p(t) and estimate the time such that 80% of the population to hear the rumor.

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Problem 66E
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Sect-6.1 P-1ESect-6.1 P-2ESect-6.1 P-3ESect-6.1 P-4ESect-6.1 P-5ESect-6.1 P-6ESect-6.1 P-7ESect-6.1 P-8ESect-6.1 P-9ESect-6.1 P-10E
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P-42AESect-6.4 P-43AESect-6.4 P-44AESect-6.4 P-45AESect-6.4 P-46AESect-6.4 P-47AESect-6.4 P-48AESect-6.4 P-49AESect-6.4 P-50AESect-6.4 P-51AESect-6.4 P-52AESect-6.4 P-53AESect-6.4 P-54AESect-6.4 P-55AESect-6.4 P-56AESect-6.4 P-57AESect-6.4 P-58AESect-6.4 P-59AESect-6.4 P-60AESect-6.4 P-61AESect-6.4 P-62AESect-6.4 P-63AESect-6.4 P-67AESect-6.4 P-68AESect-6.4 P-69AESect-6.4 P-70AESect-6.5 P-1ESect-6.5 P-2ESect-6.5 P-3ESect-6.5 P-4ESect-6.5 P-5ESect-6.5 P-6ESect-6.5 P-7ESect-6.5 P-8ESect-6.5 P-9ESect-6.5 P-10ESect-6.5 P-11ESect-6.5 P-12ESect-6.5 P-13ESect-6.5 P-14ESect-6.5 P-15ESect-6.5 P-16ESect-6.5 P-17ESect-6.5 P-18ESect-6.5 P-19ESect-6.5 P-20ESect-6.5 P-21ESect-6.5 P-22ESect-6.6 P-1ESect-6.6 P-2ESect-6.6 P-3ESect-6.6 P-4ESect-6.6 P-5ESect-6.6 P-6ESect-6.6 P-7ESect-6.6 P-8ESect-6.6 P-9ESect-6.6 P-10ESect-6.6 P-11ESect-6.6 P-12ESect-6.6 P-13ESect-6.6 P-14ESect-6.6 P-15ESect-6.6 P-16ESect-6.6 P-17ESect-6.6 P-18ESect-6.6 P-19ESect-6.6 P-20ESect-6.6 P-21ESect-6.6 P-22ESect-6.6 P-23ESect-6.6 P-24ESect-6.6 P-25ESect-6.6 P-26ESect-6.6 P-27ESect-6.6 P-28ESect-6.6 P-29ESect-6.6 P-30ESect-6.6 P-31ESect-6.6 P-32ESect-6.6 P-33ESect-6.6 P-34ESect-6.6 P-35ESect-6.6 P-36ESect-6.6 P-37ESect-6.6 P-38ESect-6.6 P-39ESect-6.6 P-40ESect-6.6 P-41ESect-6.6 P-42ESect-6.6 P-43ESect-6.6 P-44ESect-6.6 P-45ESect-6.6 P-46ESect-6.6 P-47ESect-6.6 P-48ESect-6.6 P-49ESect-6.6 P-50ESect-6.6 P-51ESect-6.6 P-52ESect-6.6 P-53ESect-6.6 P-54ESect-6.6 P-57ESect-6.6 P-58ESect-6.6 P-59ESect-6.6 P-60ESect-6.6 P-61ESect-6.6 P-62ESect-6.6 P-63ESect-6.6 P-64ESect-6.6 P-65ESect-6.6 P-66ESect-6.6 P-67ESect-6.6 P-68ESect-6.6 P-69ESect-6.6 P-70ESect-6.6 P-71ESect-6.6 P-72ESect-6.6 P-73ESect-6.6 P-74ESect-6.6 P-75ESect-6.6 P-76ESect-6.6 P-77ESect-6.6 P-78ESect-6.6 P-79ESect-6.6 P-80ESect-6.7 P-1ESect-6.7 P-2ESect-6.7 P-3ESect-6.7 P-4ESect-6.7 P-5ESect-6.7 P-6ESect-6.7 P-7ESect-6.7 P-8ESect-6.7 P-9ESect-6.7 P-10ESect-6.7 P-11ESect-6.7 P-12ESect-6.7 P-13ESect-6.7 P-14ESect-6.7 P-15ESect-6.7 P-16ESect-6.7 P-17ESect-6.7 P-18ESect-6.7 P-19ESect-6.7 P-20ESect-6.7 P-21ESect-6.7 P-22ESect-6.7 P-23ESect-6.7 P-24ESect-6.7 P-25ESect-6.7 P-26ESect-6.7 P-27ESect-6.7 P-28ESect-6.7 P-29ESect-6.7 P-30ESect-6.7 P-31ESect-6.7 P-32ESect-6.7 P-33ESect-6.7 P-34ESect-6.7 P-35ESect-6.7 P-36ESect-6.7 P-37ESect-6.7 P-38ESect-6.7 P-39ESect-6.7 P-40ESect-6.7 P-41ESect-6.7 P-42ESect-6.7 P-43ESect-6.7 P-44ESect-6.7 P-45ESect-6.7 P-46ESect-6.7 P-47ESect-6.7 P-48ESect-6.7 P-49ESect-6.7 P-50ESect-6.7 P-51ESect-6.7 P-52ESect-6.7 P-53ESect-6.7 P-54ESect-6.7 P-55ESect-6.7 P-56ESect-6.7 P-57ESect-6.7 P-58ESect-6.7 P-59ESect-6.7 P-60ESect-6.7 P-61ESect-6.7 P-62ESect-6.7 P-63ESect-6.7 P-64ESect-6.7 P-65ESect-6.7 P-66ESect-6.7 P-67ESect-6.7 P-68ESect-6.7 P-69ESect-6.7 P-70ESect-6.7 P-71ESect-6.8 P-1ESect-6.8 P-2ESect-6.8 P-3ESect-6.8 P-4ESect-6.8 P-5ESect-6.8 P-6ESect-6.8 P-7ESect-6.8 P-8ESect-6.8 P-9ESect-6.8 P-10ESect-6.8 P-11ESect-6.8 P-12ESect-6.8 P-13ESect-6.8 P-14ESect-6.8 P-15ESect-6.8 P-16ESect-6.8 P-17ESect-6.8 P-18ESect-6.8 P-19ESect-6.8 P-20ESect-6.8 P-21ESect-6.8 P-22ESect-6.8 P-23ESect-6.8 P-24ESect-6.8 P-25ESect-6.8 P-26ESect-6.8 P-27ESect-6.8 P-28ESect-6.8 P-29ESect-6.8 P-30ESect-6.8 P-31ESect-6.8 P-32ESect-6.8 P-33ESect-6.8 P-34ESect-6.8 P-35ESect-6.8 P-36ESect-6.8 P-37ESect-6.8 P-38ESect-6.8 P-39ESect-6.8 P-40ESect-6.8 P-41ESect-6.8 P-42ESect-6.8 P-43ESect-6.8 P-44ESect-6.8 P-45ESect-6.8 P-46ESect-6.8 P-47ESect-6.8 P-48ESect-6.8 P-49ESect-6.8 P-50ESect-6.8 P-51ESect-6.8 P-52ESect-6.8 P-53ESect-6.8 P-54ESect-6.8 P-55ESect-6.8 P-56ESect-6.8 P-57ESect-6.8 P-58ESect-6.8 P-59ESect-6.8 P-60ESect-6.8 P-61ESect-6.8 P-62ESect-6.8 P-63ESect-6.8 P-64ESect-6.8 P-65ESect-6.8 P-66ESect-6.8 P-67ESect-6.8 P-68ESect-6.8 P-69ESect-6.8 P-70ESect-6.8 P-71ESect-6.8 P-72ESect-6.8 P-73ESect-6.8 P-74ESect-6.8 P-75ESect-6.8 P-76ESect-6.8 P-77ESect-6.8 P-78ESect-6.8 P-79ESect-6.8 P-80ESect-6.8 P-81ESect-6.8 P-82ESect-6.8 P-86ESect-6.8 P-87ESect-6.8 P-88ESect-6.8 P-89ESect-6.8 P-90ESect-6.8 P-91ESect-6.8 P-92ESect-6.8 P-93ESect-6.8 P-94ESect-6.8 P-95ESect-6.8 P-96ESect-6.8 P-97ESect-6.8 P-98ESect-6.8 P-99ESect-6.8 P-100ESect-6.8 P-101ESect-6.8 P-102ESect-6.8 P-103ESect-6.8 P-104ECh-6 P-1RCCCh-6 P-2RCCCh-6 P-3RCCCh-6 P-4RCCCh-6 P-5RCCCh-6 P-6RCCCh-6 P-7RCCCh-6 P-8RCCCh-6 P-9RCCCh-6 P-1RQCh-6 P-2RQCh-6 P-3RQCh-6 P-4RQCh-6 P-5RQCh-6 P-6RQCh-6 P-7RQCh-6 P-8RQCh-6 P-9RQCh-6 P-10RQCh-6 P-11RQCh-6 P-12RQCh-6 P-13RQCh-6 P-14RQCh-6 P-15RQCh-6 P-16RQCh-6 P-17RQCh-6 P-18RQCh-6 P-19RQCh-6 P-1RECh-6 P-2RECh-6 P-3RECh-6 P-4RECh-6 P-5RECh-6 P-6RECh-6 P-7RECh-6 P-8RECh-6 P-9RECh-6 P-10RECh-6 P-11RECh-6 P-12RECh-6 P-13RECh-6 P-14RECh-6 P-15RECh-6 P-16RECh-6 P-17RECh-6 P-18RECh-6 P-19RECh-6 P-20RECh-6 P-21RECh-6 P-22RECh-6 P-23RECh-6 P-24RECh-6 P-25RECh-6 P-26RECh-6 P-27RECh-6 P-28RECh-6 P-29RECh-6 P-30RECh-6 P-31RECh-6 P-32RECh-6 P-33RECh-6 P-34RECh-6 P-35RECh-6 P-36RECh-6 P-37RECh-6 P-38RECh-6 P-39RECh-6 P-40RECh-6 P-41RECh-6 P-42RECh-6 P-43RECh-6 P-44RECh-6 P-45RECh-6 P-46RECh-6 P-47RECh-6 P-48RECh-6 P-49RECh-6 P-50RECh-6 P-51RECh-6 P-52RECh-6 P-53RECh-6 P-54RECh-6 P-55RECh-6 P-56RECh-6 P-57RECh-6 P-58RECh-6 P-59RECh-6 P-60RECh-6 P-61RECh-6 P-62RECh-6 P-63RECh-6 P-64RECh-6 P-65RECh-6 P-66RECh-6 P-67RECh-6 P-68RECh-6 P-69RECh-6 P-70RECh-6 P-71RECh-6 P-72RECh-6 P-73RECh-6 P-74RECh-6 P-75RECh-6 P-76RECh-6 P-77RECh-6 P-78RECh-6 P-79RECh-6 P-80RECh-6 P-81RECh-6 P-82RECh-6 P-83RECh-6 P-84RECh-6 P-85RECh-6 P-86RECh-6 P-87RECh-6 P-88RECh-6 P-89RECh-6 P-90RECh-6 P-91RECh-6 P-92RECh-6 P-93RECh-6 P-94RECh-6 P-95RECh-6 P-96RECh-6 P-97RECh-6 P-98RECh-6 P-99RECh-6 P-100RECh-6 P-101RECh-6 P-102RECh-6 P-103RECh-6 P-104RECh-6 P-105RECh-6 P-106RECh-6 P-107RECh-6 P-108RECh-6 P-109RECh-6 P-110RECh-6 P-111RECh-6 P-112RECh-6 P-113RECh-6 P-114RECh-6 P-115RECh-6 P-116RECh-6 P-117RECh-6 P-118RECh-6 P-119RECh-6 P-120RECh-6 P-121RECh-6 P-122RECh-6 P-1PCh-6 P-2PCh-6 P-3PCh-6 P-4PCh-6 P-5PCh-6 P-6PCh-6 P-7PCh-6 P-8PCh-6 P-9PCh-6 P-10PCh-6 P-11PCh-6 P-12PCh-6 P-13PCh-6 P-14PCh-6 P-15PCh-6 P-16PCh-6 P-17PCh-6 P-18PCh-6 P-19PCh-6 P-20P

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