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product determines that P percent of the potential market is aware of the product t weeks after the advertising campaign begins. (a) What happens to the percent of people who are aware of the product in the long run? As time passes, the percent of people aware of the product approaches approximately____%. (b) What happens to the rate of change of the percent of people who are aware of the product in the long run? As time passes, the rate of change of the percent of people

product determines that P percent of the potential market is aware of the product t weeks after the advertising campaign begins. (a) What happens to the percent of people who are aware of the product in the long run? As time passes, the percent of people aware of the product approaches approximately____%. (b) What happens to the rate of change of the percent of people who are aware of the product in the long run? As time passes, the rate of change of the percent of people

Calculus: Early Transcendentals
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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The advertising manager for a new product determines that P percent of the potential market is aware of the product t weeks after the advertising campaign begins. (a) What happens to the percent of people who are aware of the product in the long run? As time passes, the percent of people aware of the product approaches approximately____%. (b) What happens to the rate of change of the percent of people who are aware of the product in the long run? As time passes, the rate of change of the percent of people aware of the product approaches ____%.
The advertising manager for a new product determines that \( P \) percent of the potential market is aware of the product \( t \) weeks after the advertising campaign begins. **Market Awareness Graph Explanation:** - The graph titled "Market Awareness" plots the percentage \( P \) of market awareness on the vertical axis against the number of weeks \( t \) on the horizontal axis. - The graph shows an S-shaped curve, indicating a rapid increase in awareness initially, which gradually levels off over time. - The awareness percentage starts at 10% and increases quickly, reaching around 70% by the 10th week. - As more weeks pass, the graph continues to rise but at a decreasing rate, approaching a maximum of about 95% around the 60th week. **Analysis Questions:** (a) **What happens to the percent of people who are aware of the product in the long run?** - As time passes, the percent of people aware of the product approaches approximately 95%. (b) **What happens to the rate of change of the percent of people who are aware of the product in the long run?** - As time passes, the rate of change of the percentage of people aware of the product approaches 0% per week, indicating the market awareness stabilizes.
Transcribed Image Text:The advertising manager for a new product determines that \( P \) percent of the potential market is aware of the product \( t \) weeks after the advertising campaign begins. **Market Awareness Graph Explanation:** - The graph titled "Market Awareness" plots the percentage \( P \) of market awareness on the vertical axis against the number of weeks \( t \) on the horizontal axis. - The graph shows an S-shaped curve, indicating a rapid increase in awareness initially, which gradually levels off over time. - The awareness percentage starts at 10% and increases quickly, reaching around 70% by the 10th week. - As more weeks pass, the graph continues to rise but at a decreasing rate, approaching a maximum of about 95% around the 60th week. **Analysis Questions:** (a) **What happens to the percent of people who are aware of the product in the long run?** - As time passes, the percent of people aware of the product approaches approximately 95%. (b) **What happens to the rate of change of the percent of people who are aware of the product in the long run?** - As time passes, the rate of change of the percentage of people aware of the product approaches 0% per week, indicating the market awareness stabilizes.
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