### Matching Exponential Functions to GraphsIn 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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Answered: Use the graph to match each equation…

Math

Algebra

Use the graph to match each equation with the correct function.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter1: Expressions And Functions

Section1.8: Interpreting Graphs Of Functions

Problem 4CYU

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Concept explainers

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.

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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

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