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Suppose you're going to sell a certain product, and your marketing team has determined that the maximum number of units of the product that can be sold (based on number of households, desirability, and so on) is given by a constant M>0, and that the rate of increase in unit sales will be proportional to the difference between M and the number of units that have currently been sold. Then the cumulative number of units >0, sold for any time t will be given by a function of the form: A. U(t) = Aekt where A is some undetermined constant, and k> 0 is some proportionality constant. B. U(t) = Aekt – M, where A is some undetermined constant, and k > 0 is some proportionality constant. C. U(t) = Ae-kt - M, where A is some undetermined constant, and k > 0 is some proportionality constant. D. U(t) = Ae¯kt + M, where A is some undetermined constant, and k> 0 is some proportionality constant. E. U(t) = Aekt + M, where A is some undetermined constant, and k> 0 is some proportionality constant.

Suppose you're going to sell a certain product, and your marketing team has determined that the maximum number of units of the product that can be sold (based on number of households, desirability, and so on) is given by a constant M>0, and that the rate of increase in unit sales will be proportional to the difference between M and the number of units that have currently been sold. Then the cumulative number of units >0, sold for any time t will be given by a function of the form: A. U(t) = Aekt where A is some undetermined constant, and k> 0 is some proportionality constant. B. U(t) = Aekt – M, where A is some undetermined constant, and k > 0 is some proportionality constant. C. U(t) = Ae-kt - M, where A is some undetermined constant, and k > 0 is some proportionality constant. D. U(t) = Ae¯kt + M, where A is some undetermined constant, and k> 0 is some proportionality constant. E. U(t) = Aekt + M, where A is some undetermined constant, and k> 0 is some proportionality constant.

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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### Determining the Sales Function for a Product **Scenario:** Suppose you're going to sell a certain product, and your marketing team has determined that the maximum number of units of the product that can be sold (based on the number of households, desirability, and so on) is given by a constant \( M > 0 \). Additionally, the rate of increase in unit sales will be proportional to the difference between \( M \) and the number of units that have currently been sold. **Objective:** The cumulative number of units \( U \), sold for any time \( t \) (where \( t > 0 \)), will be given by a function of the form: ### Options: - **A.** \( U(t) = Ae^{kt} \) - where \( A \) is some undetermined constant, and \( k > 0 \) is some proportionality constant. - **B.** \( U(t) = Ae^{kt} - M \) - where \( A \) is some undetermined constant, and \( k > 0 \) is some proportionality constant. - **C.** \( U(t) = Ae^{-kt} - M \) - where \( A \) is some undetermined constant, and \( k > 0 \) is some proportionality constant. - **D.** \( U(t) = Ae^{-kt} + M \) - where \( A \) is some undetermined constant, and \( k > 0 \) is some proportionality constant. - **E.** \( U(t) = Ae^{kt} + M \) - where \( A \) is some undetermined constant, and \( k > 0 \) is some proportionality constant.
Transcribed Image Text:### Determining the Sales Function for a Product **Scenario:** Suppose you're going to sell a certain product, and your marketing team has determined that the maximum number of units of the product that can be sold (based on the number of households, desirability, and so on) is given by a constant \( M > 0 \). Additionally, the rate of increase in unit sales will be proportional to the difference between \( M \) and the number of units that have currently been sold. **Objective:** The cumulative number of units \( U \), sold for any time \( t \) (where \( t > 0 \)), will be given by a function of the form: ### Options: - **A.** \( U(t) = Ae^{kt} \) - where \( A \) is some undetermined constant, and \( k > 0 \) is some proportionality constant. - **B.** \( U(t) = Ae^{kt} - M \) - where \( A \) is some undetermined constant, and \( k > 0 \) is some proportionality constant. - **C.** \( U(t) = Ae^{-kt} - M \) - where \( A \) is some undetermined constant, and \( k > 0 \) is some proportionality constant. - **D.** \( U(t) = Ae^{-kt} + M \) - where \( A \) is some undetermined constant, and \( k > 0 \) is some proportionality constant. - **E.** \( U(t) = Ae^{kt} + M \) - where \( A \) is some undetermined constant, and \( k > 0 \) is some proportionality constant.
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