A rumor spreads among a group of 400 people. The number of people who have heard the rumor after t hours is given by: 400 N(t) = %3| (1+399e-0.05t ) After how many hours is the rumor spreading fastest? Round answer to the nearest hour Select one: O 400 hours O 180 hours 15 hours 60 hours O 120 hours
A rumor spreads among a group of 400 people. The number of people who have heard the rumor after t hours is given by: 400 N(t) = %3| (1+399e-0.05t ) After how many hours is the rumor spreading fastest? Round answer to the nearest hour Select one: O 400 hours O 180 hours 15 hours 60 hours O 120 hours
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Rumor Spreading Model**
A rumor spreads among a group of 400 people. The number of people who have heard the rumor after \( t \) hours is given by the function:
\[
N(t) = \frac{400}{1 + 399e^{-0.05t}}
\]
**Question:** After how many hours is the rumor spreading fastest? Round your answer to the nearest hour.
**Options:**
- ○ 400 hours
- ○ 180 hours
- ○ 15 hours
- ○ 60 hours
- ○ 120 hours
**Explanation:**
This problem involves finding the time at which the rumor spreads at its maximum rate. This usually corresponds to the inflection point of the curve represented by the given logistic function, often occurring halfway through the spread.
Consider analyzing the derivative of \( N(t) \) to find the maximum rate of change.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F59e80801-02d9-473f-80ed-2b97fa470de7%2F6ae6f671-d281-4d71-b4f2-d10bcd4954be%2Fktxf049_processed.png&w=3840&q=75)
Transcribed Image Text:**Rumor Spreading Model**
A rumor spreads among a group of 400 people. The number of people who have heard the rumor after \( t \) hours is given by the function:
\[
N(t) = \frac{400}{1 + 399e^{-0.05t}}
\]
**Question:** After how many hours is the rumor spreading fastest? Round your answer to the nearest hour.
**Options:**
- ○ 400 hours
- ○ 180 hours
- ○ 15 hours
- ○ 60 hours
- ○ 120 hours
**Explanation:**
This problem involves finding the time at which the rumor spreads at its maximum rate. This usually corresponds to the inflection point of the curve represented by the given logistic function, often occurring halfway through the spread.
Consider analyzing the derivative of \( N(t) \) to find the maximum rate of change.
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