Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Matching Exponential Functions to Graphs
In this exercise, you are provided with a graph and a set of exponential equations. Your task is to match each equation with the correct function on the graph. The graph contains four curves, each labeled with a letter: \( f \), \( g \), \( h \), and \( j \).
#### Graph Explanation:
- The graph is plotted on a coordinate plane with the \( y \)-axis ranging from 0 to 10 and the \( x \)-axis ranging from 0 to 16.
- Each curve on the graph represents an exponential decay function, characterized by the equation \( y = ae^{-bx} \).
- The colors associated with each curve are as follows:
- \( g \) is the blue curve
- \( f \) is the green curve
- \( h \) is the purple curve
- \( j \) is the red curve
#### Equations to be Matched:
1. \( y = 14e^{-0.75x} \)
2. \( y = 8e^{-0.2x} \)
3. \( y = 8e^{-0.8x} \)
4. \( y = 14e^{-0.1x} \)
#### Steps to Match Equations with Functions:
1. Evaluate the initial values (when \( x = 0 \)) to identify the starting point on the \( y \)-axis for each equation.
2. Analyze the rate of decay (the exponent's coefficient) to match the curve’s steepness.
### Interactive Matching:
Use the matching tools provided below to connect each equation with the corresponding curve label:
- [Equation 1: \( y = 14e^{-0.75x} \) ] ⟶ [ f ] [ g ] [ h ] [ j ]
- [Equation 2: \( y = 8e^{-0.2x} \) ] ⟶ [ f ] [ g ] [ h ] [ j ]
- [Equation 3: \( y = 8e^{-0.8x} \) ] ⟶ [ f ] [ g ] [ h ] [ j ]
- [Equation 4: \( y = 14e^{-0.1x} \) ] ⟶ [ f ] [ g ] [ h ] [ j ]
By carefully analyzing the initial points and](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1f0eb3d4-5c31-491e-b1a2-5741c316a209%2Fa84a7b0d-c00d-4bb4-ae6a-8c137d4be551%2Fw1wv129_processed.png&w=3840&q=75)
Transcribed Image Text:### Matching Exponential Functions to Graphs
In this exercise, you are provided with a graph and a set of exponential equations. Your task is to match each equation with the correct function on the graph. The graph contains four curves, each labeled with a letter: \( f \), \( g \), \( h \), and \( j \).
#### Graph Explanation:
- The graph is plotted on a coordinate plane with the \( y \)-axis ranging from 0 to 10 and the \( x \)-axis ranging from 0 to 16.
- Each curve on the graph represents an exponential decay function, characterized by the equation \( y = ae^{-bx} \).
- The colors associated with each curve are as follows:
- \( g \) is the blue curve
- \( f \) is the green curve
- \( h \) is the purple curve
- \( j \) is the red curve
#### Equations to be Matched:
1. \( y = 14e^{-0.75x} \)
2. \( y = 8e^{-0.2x} \)
3. \( y = 8e^{-0.8x} \)
4. \( y = 14e^{-0.1x} \)
#### Steps to Match Equations with Functions:
1. Evaluate the initial values (when \( x = 0 \)) to identify the starting point on the \( y \)-axis for each equation.
2. Analyze the rate of decay (the exponent's coefficient) to match the curve’s steepness.
### Interactive Matching:
Use the matching tools provided below to connect each equation with the corresponding curve label:
- [Equation 1: \( y = 14e^{-0.75x} \) ] ⟶ [ f ] [ g ] [ h ] [ j ]
- [Equation 2: \( y = 8e^{-0.2x} \) ] ⟶ [ f ] [ g ] [ h ] [ j ]
- [Equation 3: \( y = 8e^{-0.8x} \) ] ⟶ [ f ] [ g ] [ h ] [ j ]
- [Equation 4: \( y = 14e^{-0.1x} \) ] ⟶ [ f ] [ g ] [ h ] [ j ]
By carefully analyzing the initial points and
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