45; and interpret the results. 46. Supply. A supply function for a certain product is given by S(p) = 0.08p³ + 2p² + 10p + 11, where S(p) is the number of items produced when the price is p dollars. Use S'(p) to estimate how many more units a producer will supply when the price changes from $18.00 per unit to $18.20 per unit.
45; and interpret the results. 46. Supply. A supply function for a certain product is given by S(p) = 0.08p³ + 2p² + 10p + 11, where S(p) is the number of items produced when the price is p dollars. Use S'(p) to estimate how many more units a producer will supply when the price changes from $18.00 per unit to $18.20 per unit.
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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How would you solve number 46?
![**Educational Website Content: Mathematical Concepts and Applications**
### 44. Marginal Profit
*Tuttle Automotive manufactures seat covers. The company estimates the cost of producing x thousand seat covers with the function*:
\[ C(x) = 0.0025x^3 + 0.3x^2 - 3.4x + 15, \]
*where C(x) is in thousands of dollars.*
- **Tasks:**
- **(a)** Calculate the cost of producing 6000 seat covers.
- **(b)** Identify the marginal cost when 6000 seat covers are produced.
- **(c)** Use the results from (a) and (b) to estimate the cost to produce 7000 seat covers.
### 45. Marginal Productivity
*An employee’s monthly productivity, M(t), in terms of units produced, is determined by*:
\[ M(t) = -2t^2 + 100t + 180, \]
*with t representing years of employment.*
- **Tasks:**
- **(a)** Determine productivity after 5, 10, 25, and 45 years of employment.
- **(b)** Calculate the marginal productivity.
- **(c)** Compute the marginal productivity at \( t = 5, t = 10, \) and \( t = 25, t = 45; \) and interpret the outcomes.
### 46. Supply
*A supply function for a product is defined as*:
\[ S(p) = 0.08p^3 + 2p^2 + 10p + 11, \]
*where S(p) indicates the number of items produced when the price is p dollars. Use S'(p) to predict the change in units produced as the price shifts from $18.00 to $18.20 per unit.*
### 47. Gross Domestic Product
*The U.S. gross domestic product, P(x), in billions of current dollars, follows*:
\[ P(x) = 1.025e^{0.0247x}, \]
*where x signifies years since 1990. (Source: U.S. Bureau for Economic Analysis.) Utilize P'(x) to estimate GDP growth from 2019 to 2020.*
### 48. Advertising
*Norris Inc. predicts its sales, N(x), in units, in](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F631ebc5c-4ef7-493e-ad4a-59361e0347ad%2F7c58ef67-81cb-45d8-8356-d6997bdcee1e%2F4w6w1ck_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Website Content: Mathematical Concepts and Applications**
### 44. Marginal Profit
*Tuttle Automotive manufactures seat covers. The company estimates the cost of producing x thousand seat covers with the function*:
\[ C(x) = 0.0025x^3 + 0.3x^2 - 3.4x + 15, \]
*where C(x) is in thousands of dollars.*
- **Tasks:**
- **(a)** Calculate the cost of producing 6000 seat covers.
- **(b)** Identify the marginal cost when 6000 seat covers are produced.
- **(c)** Use the results from (a) and (b) to estimate the cost to produce 7000 seat covers.
### 45. Marginal Productivity
*An employee’s monthly productivity, M(t), in terms of units produced, is determined by*:
\[ M(t) = -2t^2 + 100t + 180, \]
*with t representing years of employment.*
- **Tasks:**
- **(a)** Determine productivity after 5, 10, 25, and 45 years of employment.
- **(b)** Calculate the marginal productivity.
- **(c)** Compute the marginal productivity at \( t = 5, t = 10, \) and \( t = 25, t = 45; \) and interpret the outcomes.
### 46. Supply
*A supply function for a product is defined as*:
\[ S(p) = 0.08p^3 + 2p^2 + 10p + 11, \]
*where S(p) indicates the number of items produced when the price is p dollars. Use S'(p) to predict the change in units produced as the price shifts from $18.00 to $18.20 per unit.*
### 47. Gross Domestic Product
*The U.S. gross domestic product, P(x), in billions of current dollars, follows*:
\[ P(x) = 1.025e^{0.0247x}, \]
*where x signifies years since 1990. (Source: U.S. Bureau for Economic Analysis.) Utilize P'(x) to estimate GDP growth from 2019 to 2020.*
### 48. Advertising
*Norris Inc. predicts its sales, N(x), in units, in
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