Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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Suppose \( y_0 \) is the \( y \)-coordinate of the point of intersection of the graphs below. Complete the statement below in order to correctly describe what happens to \( y_0 \) if the value of \( r \) (in the blue graph of \( f(t) = a(1 + rt)^r \) below) is increased, and all other quantities remain the same.

As \( r \) increases, does the value of \( y_0 \) increase, decrease, or remain the same? [Choose]

**Graph Explanation:**

The graph consists of two functions:

1. **Blue curve**: Represents the function \( f(t) = a(1 + rt)^r \). This graph is upward-curving, indicating exponential growth as \( t \) increases.

2. **Red line**: Represents the function \( g(t) = b + mt \). This graph is a straight line, indicating linear growth.

The point of intersection between the blue curve and the red line is labeled as \( (t_0, y_0) \).

**Note:** To view a larger version of the graph, click on the image.
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Transcribed Image Text:Suppose \( y_0 \) is the \( y \)-coordinate of the point of intersection of the graphs below. Complete the statement below in order to correctly describe what happens to \( y_0 \) if the value of \( r \) (in the blue graph of \( f(t) = a(1 + rt)^r \) below) is increased, and all other quantities remain the same. As \( r \) increases, does the value of \( y_0 \) increase, decrease, or remain the same? [Choose] **Graph Explanation:** The graph consists of two functions: 1. **Blue curve**: Represents the function \( f(t) = a(1 + rt)^r \). This graph is upward-curving, indicating exponential growth as \( t \) increases. 2. **Red line**: Represents the function \( g(t) = b + mt \). This graph is a straight line, indicating linear growth. The point of intersection between the blue curve and the red line is labeled as \( (t_0, y_0) \). **Note:** To view a larger version of the graph, click on the image.
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