Cost, revenue, and profit are in dollars and x is the number of units. The average cost of a product changes at the rate C'(x) = 30 + 100 and the average cost of 10 units is $50.00. (a) Find the average cost function. (b) Find the average cost of 30 units. (Round your answer to two decimal places.) $
Cost, revenue, and profit are in dollars and x is the number of units. The average cost of a product changes at the rate C'(x) = 30 + 100 and the average cost of 10 units is $50.00. (a) Find the average cost function. (b) Find the average cost of 30 units. (Round your answer to two decimal places.) $
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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![### Understanding Average Cost in Economics
In this exercise, we will explore the concept of average cost in the context of economic analysis. Here, cost, revenue, and profit are measured in dollars, and \( x \) represents the number of units produced.
#### Problem Statement
The rate at which the average cost of a product changes is given by:
\[
\overline{C}'(x) = \frac{-30}{x^2} + \frac{1}{10}
\]
Additionally, the average cost of producing 10 units is specified as $50.00.
#### Tasks
(a) **Find the Average Cost Function:**
To determine the average cost function \( \overline{C} \), we need to integrate the given rate of change of the average cost.
\[
\overline{C} = \ \_\_\_\_\_\_\_\_\_\_\_\_
\]
(b) **Find the Average Cost of 30 Units:**
Calculate the average cost for producing 30 units by substituting \( x = 30 \) into the derived average cost function. Round your answer to two decimal places.
\[
\$ \ \_\_\_\_\_\_\_\_
\]
Use this guide to understand how changes in production levels can affect the average cost and apply these calculations to real-world situations for improved financial predictions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ac160ea-586d-4b6a-bc87-d7b74a3b50c7%2F022003bf-312d-425c-a695-d5e1c71700a0%2Fp89bjbh_processed.png&w=3840&q=75)
Transcribed Image Text:### Understanding Average Cost in Economics
In this exercise, we will explore the concept of average cost in the context of economic analysis. Here, cost, revenue, and profit are measured in dollars, and \( x \) represents the number of units produced.
#### Problem Statement
The rate at which the average cost of a product changes is given by:
\[
\overline{C}'(x) = \frac{-30}{x^2} + \frac{1}{10}
\]
Additionally, the average cost of producing 10 units is specified as $50.00.
#### Tasks
(a) **Find the Average Cost Function:**
To determine the average cost function \( \overline{C} \), we need to integrate the given rate of change of the average cost.
\[
\overline{C} = \ \_\_\_\_\_\_\_\_\_\_\_\_
\]
(b) **Find the Average Cost of 30 Units:**
Calculate the average cost for producing 30 units by substituting \( x = 30 \) into the derived average cost function. Round your answer to two decimal places.
\[
\$ \ \_\_\_\_\_\_\_\_
\]
Use this guide to understand how changes in production levels can affect the average cost and apply these calculations to real-world situations for improved financial predictions.
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