**For Exercises 69 and 70, refer to the following:**A company’s total revenue $ R $ (in millions of dollars) is related to its advertising costs $ x $ (in thousands of dollars). The relationship between revenue $ R $ and advertising costs $ x $ is illustrated in the graph.**Graph Detail:**The graph plots Revenue $ R $ in millions of dollars on the vertical axis (y-axis) against Advertising Costs $ x $ in thousands of dollars on the horizontal axis (x-axis). The curve starts at the origin, rises to a peak, and then declines, forming a parabolic shape.- The horizontal axis (x-axis) is labeled "Advertising Costs (in thousands of dollars)" and is marked at intervals of 100, ranging from 0 to 600.- The vertical axis (y-axis) is labeled "Revenue (in millions of dollars)" and is marked at intervals of 5, ranging from 0 to 50.- The curve starts near the origin, peaks at approximately $ x = 300 $ to $ x = 400 $, reaching a revenue of around $ R = 40 $, and then declines to touch near the horizontal axis somewhere between $ x = 500 $ and $ x = 600 $.**Questions:**69. **Business.** Analyze the graph of the revenue function. - **a.** Determine the intervals on which revenue is increasing and those on which it is decreasing. - **b.** Identify the zeros of the function. Interpret the meaning of zeros for this function.

69.a) Revenue is increasing in the interval of (0,400) Revenue is decreasing in the interval of…

For Exercises 69 and 70, refer to the following: A company's total revenue R (in millions of dollars) is related to its advertising costs x (in thousands of dollars). The relationship between revenue R and advertising costs x is illustrated in the graph.

For Exercises 69 and 70, refer to the following: A company's total revenue R (in millions of dollars) is related to its advertising costs x (in thousands of dollars). The relationship between revenue R and advertising costs x is illustrated in the graph.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.

Question

100%

**For Exercises 69 and 70, refer to the following:**

A company’s total revenue $ R $ (in millions of dollars) is related to its advertising costs $ x $ (in thousands of dollars). The relationship between revenue $ R $ and advertising costs $ x $ is illustrated in the graph.

**Graph Detail:**

The graph plots Revenue $ R $ in millions of dollars on the vertical axis (y-axis) against Advertising Costs $ x $ in thousands of dollars on the horizontal axis (x-axis). The curve starts at the origin, rises to a peak, and then declines, forming a parabolic shape.

- The horizontal axis (x-axis) is labeled "Advertising Costs (in thousands of dollars)" and is marked at intervals of 100, ranging from 0 to 600.
- The vertical axis (y-axis) is labeled "Revenue (in millions of dollars)" and is marked at intervals of 5, ranging from 0 to 50.
- The curve starts near the origin, peaks at approximately $ x = 300 $ to $ x = 400 $, reaching a revenue of around $ R = 40 $, and then declines to touch near the horizontal axis somewhere between $ x = 500 $ and $ x = 600 $.

**Questions:**

69. **Business.** Analyze the graph of the revenue function.

- **a.** Determine the intervals on which revenue is increasing and those on which it is decreasing.
- **b.** Identify the zeros of the function. Interpret the meaning of zeros for this function.

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