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4. A store finds that its sales decline after their ad campaign ends. The rate at which the daily sales decline is given as S'(t) = 225e-0.25t days since the ads quit running. Suppose that their daily sales are 3700 units at the time the campaign ends (t= 0). Find: a. The function that describes the total daily sales, or S(t). b. What the daily sales will be 7 days after the ads stop running. - 210, wheret is the number of

4. A store finds that its sales decline after their ad campaign ends. The rate at which the daily sales decline is given as S'(t) = 225e-0.25t days since the ads quit running. Suppose that their daily sales are 3700 units at the time the campaign ends (t= 0). Find: a. The function that describes the total daily sales, or S(t). b. What the daily sales will be 7 days after the ads stop running. - 210, wheret is the number of

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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Please I can really use some help to find out how to do this problem, i also provide the formula sheet i have to follow to figure it out
**Your "Tattoo" Cheat Sheet - Use Often!** --- ### The Basics - \( x \rightarrow f(x) \rightarrow y \) (y can be \( +, \emptyset, - \)) - \( x \rightarrow f'(x) \rightarrow \) Slope (Slope can be \( +, \emptyset, - \)) - \( \emptyset = \) max or min or H.P.I. - \( x \rightarrow f''(x) \rightarrow \) Concavity (Concavity is \( \cup, \emptyset, \cap \)) - \( \emptyset \) is point of inflection **Derivatives:** 1. \( y = x^n \) \(\quad y' = nx^{n-1}\) 2. \( y = u^n \) \(\quad y' = nu^{n-1}u'\) 3. \( y = e^x \) \(\quad y' = ue^uu'\) 4. \( y = \ln u \) \(\quad y' = \frac{u'}{u}\) - \( u \) is a function, \( x \) is a variable, \( e \) and \( n \) are constants. **Integrals:** 1. \( y = \int x^n dx \rightarrow \frac{x^{n+1}}{n+1} + k, \quad n \neq -1 \) 2. \( y = \int u^n dx \rightarrow \frac{u^{n+1}}{n+1} + k, \quad n \neq -1 \) 3. \( y = \int e^u dx \rightarrow e^u + k \) 4. \( y = \int \frac{u'}{u} dx \rightarrow \ln u + k, \quad n = -1 \) **Steps for Integration:** 1. Make it pretty. Which integral? 2. Find \( u \); create \( u' \) 3. We have ____, we want ____! 4. Make it look like the template 5. Perform integral **Also:** - \( y = \int ax^n dx = a \int x^n dx \) - \( y = \int (ax^n + bx^m) dx = \int ax^n dx +
Transcribed Image Text:**Your "Tattoo" Cheat Sheet - Use Often!** --- ### The Basics - \( x \rightarrow f(x) \rightarrow y \) (y can be \( +, \emptyset, - \)) - \( x \rightarrow f'(x) \rightarrow \) Slope (Slope can be \( +, \emptyset, - \)) - \( \emptyset = \) max or min or H.P.I. - \( x \rightarrow f''(x) \rightarrow \) Concavity (Concavity is \( \cup, \emptyset, \cap \)) - \( \emptyset \) is point of inflection **Derivatives:** 1. \( y = x^n \) \(\quad y' = nx^{n-1}\) 2. \( y = u^n \) \(\quad y' = nu^{n-1}u'\) 3. \( y = e^x \) \(\quad y' = ue^uu'\) 4. \( y = \ln u \) \(\quad y' = \frac{u'}{u}\) - \( u \) is a function, \( x \) is a variable, \( e \) and \( n \) are constants. **Integrals:** 1. \( y = \int x^n dx \rightarrow \frac{x^{n+1}}{n+1} + k, \quad n \neq -1 \) 2. \( y = \int u^n dx \rightarrow \frac{u^{n+1}}{n+1} + k, \quad n \neq -1 \) 3. \( y = \int e^u dx \rightarrow e^u + k \) 4. \( y = \int \frac{u'}{u} dx \rightarrow \ln u + k, \quad n = -1 \) **Steps for Integration:** 1. Make it pretty. Which integral? 2. Find \( u \); create \( u' \) 3. We have ____, we want ____! 4. Make it look like the template 5. Perform integral **Also:** - \( y = \int ax^n dx = a \int x^n dx \) - \( y = \int (ax^n + bx^m) dx = \int ax^n dx +
**Problem 4:** A store finds that its sales decline after their ad campaign ends. The rate at which the daily sales decline is given as \( S'(t) = 225e^{-0.25t} - 210 \), where \( t \) is the number of days since the ads quit running. Suppose that their daily sales are 3700 units at the time the campaign ends (\( t = 0 \)). Find: a. The function that describes the total daily sales, or \( S(t) \). b. What the daily sales will be 7 days after the ads stop running.
Transcribed Image Text:**Problem 4:** A store finds that its sales decline after their ad campaign ends. The rate at which the daily sales decline is given as \( S'(t) = 225e^{-0.25t} - 210 \), where \( t \) is the number of days since the ads quit running. Suppose that their daily sales are 3700 units at the time the campaign ends (\( t = 0 \)). Find: a. The function that describes the total daily sales, or \( S(t) \). b. What the daily sales will be 7 days after the ads stop running.
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