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

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 40E
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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
100
90
80
70
60
50
40
30
20
10
10
20
30
40
50
60
Weeks
(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 percent of people aware of the product approaches 8
X %/week.
Percent
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 100 90 80 70 60 50 40 30 20 10 10 20 30 40 50 60 Weeks (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 percent of people aware of the product approaches 8 X %/week. Percent
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