The number of people in a town of 65,000 who have heard an important news bulletin within t hours of its first broadcast is N(t) = 65,000(1e-0.4t). Find the rate of change of the number of informed people at the following times. (Round your answers to the nearest integer.) (a) at time t = 0 people/hour (b) after 8 hours people/hour
The number of people in a town of 65,000 who have heard an important news bulletin within t hours of its first broadcast is N(t) = 65,000(1e-0.4t). Find the rate of change of the number of informed people at the following times. (Round your answers to the nearest integer.) (a) at time t = 0 people/hour (b) after 8 hours people/hour
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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![**Problem Description:**
The number of people in a town of 65,000 who have heard an important news bulletin within \( t \) hours of its first broadcast is \( N(t) = 65,000 (1 - e^{-0.4t}) \). Find the rate of change of the number of informed people at the following times. (Round your answers to the nearest integer.)
**Tasks:**
(a) At time \( t = 0 \)
\[ \boxed{\text{people/hour}} \]
(b) After 8 hours
\[ \boxed{\text{people/hour}} \]
**Explanation:**
To find the rate of change of the number of informed people, we need to compute the derivative of \( N(t) = 65,000 (1 - e^{-0.4t}) \) and evaluate it at the given times. The derivative \( N'(t) \) will give us the rate of change in people per hour.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7e0cd55c-6f84-412a-ac81-9a79eaea810f%2Fb83b3613-4399-46a6-8e82-aa8eb624b129%2Fjdkslu_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Description:**
The number of people in a town of 65,000 who have heard an important news bulletin within \( t \) hours of its first broadcast is \( N(t) = 65,000 (1 - e^{-0.4t}) \). Find the rate of change of the number of informed people at the following times. (Round your answers to the nearest integer.)
**Tasks:**
(a) At time \( t = 0 \)
\[ \boxed{\text{people/hour}} \]
(b) After 8 hours
\[ \boxed{\text{people/hour}} \]
**Explanation:**
To find the rate of change of the number of informed people, we need to compute the derivative of \( N(t) = 65,000 (1 - e^{-0.4t}) \) and evaluate it at the given times. The derivative \( N'(t) \) will give us the rate of change in people per hour.
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