### Transcription for Educational Website#### Graphs and Equations Matching ActivityThe image displays a set of five exponential graphs plotted on a coordinate system, each with distinct colors and labels. The objective is to match each given exponential equation with the corresponding graph.**Graphs:**- **Red (R)**- **Green (G)**- **Orange (O)**- **Black (K)**- **Blue (B)****Equations to Match:**1. $3(1.18)^x$2. $4(1.18)^x$3. $4(1.55)^x$4. $4(0.66)^x$**Options Corresponding to the Graphs:**- a. **Black (K)**- b. **Green (G)**- c. **Red (R)**- d. **Orange (O)**- e. **Blue (B)**#### Instructions- Each equation is associated with a dropdown to select the correct graph.- Analyze the growth rate and initial value of each equation to determine which graph corresponds to it.For educators: Use this activity to help students understand the relationship between exponential equations and their graphical representations. Discuss the effect of the base of the exponent and the initial coefficient on the shape and position of each graph. **Graph Analysis and Matching Exercise**In the graph, there are five curves labeled with different colors: red (R), orange (O), green (G), blue (B), and black (K). Each curve represents a different exponential function.Below is a list of equations. The task is to match each equation with its corresponding curve on the graph.**Equations:**1. $ f(x) = 3(1.18)^x $2. $ f(x) = 4(1.18)^x $3. $ f(x) = 4(1.55)^x $4. $ f(x) = 4(0.66)^x $5. $ f(x) = 4(0.81)^x $**Curve Matches:**- **a. Black (K)**- **b. Green (G)**- **c. Red (R)**- **d. Orange (O)**- **e. Blue (B)****Matching Results:**- $ f(x) = 3(1.18)^x $ matches with **Orange (O)**- $ f(x) = 4(1.18)^x $ matches with **Green (G)**- $ f(x) = 4(1.55)^x $ matches with **Red (R)**- $ f(x) = 4(0.66)^x $ matches with **Blue (B)**- $ f(x) = 4(0.81)^x $ matches with **Black (K)****Analysis of the Graph:**- **Red Curve (R):** Rapidly increasing function, indicative of a high growth rate.- **Orange Curve (O):** Increasing at a slower rate compared to the red curve.- **Green Curve (G):** Similar behavior to the orange curve, slightly shifted upwards.- **Blue Curve (B):** Represents a decreasing function, indicating decay.- **Black Curve (K):** Shows moderate decrease, less steep than the blue curve.This exercise helps in understanding how exponential functions are represented graphically and how different parameters affect their growth or decay rates.

To graph the function, we will look at the intersection point and slopes y=31.18xPlug x=0, for…

Answered: K В Match each equation with a graph…

K В Match each equation with a graph above dv 3(1.18)" a. black (K) cv 4(1.18)" b. green (G) c. red (R) bv 4(1.55)" d. orange (0) ev 4(0.66)" e. blue (B) av4(0.81)"

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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Concept explainers

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.

Question

### Transcription for Educational Website

#### Graphs and Equations Matching Activity

The image displays a set of five exponential graphs plotted on a coordinate system, each with distinct colors and labels. The objective is to match each given exponential equation with the corresponding graph.

**Graphs:**
- **Red (R)**
- **Green (G)**
- **Orange (O)**
- **Black (K)**
- **Blue (B)**

**Equations to Match:**
1. $3(1.18)^x$
2. $4(1.18)^x$
3. $4(1.55)^x$
4. $4(0.66)^x$

**Options Corresponding to the Graphs:**
- a. **Black (K)**
- b. **Green (G)**
- c. **Red (R)**
- d. **Orange (O)**
- e. **Blue (B)**

#### Instructions

- Each equation is associated with a dropdown to select the correct graph.
- Analyze the growth rate and initial value of each equation to determine which graph corresponds to it.

For educators: Use this activity to help students understand the relationship between exponential equations and their graphical representations. Discuss the effect of the base of the exponent and the initial coefficient on the shape and position of each graph.

**Graph Analysis and Matching Exercise**

In the graph, there are five curves labeled with different colors: red (R), orange (O), green (G), blue (B), and black (K). Each curve represents a different exponential function.

Below is a list of equations. The task is to match each equation with its corresponding curve on the graph.

**Equations:**

1. $ f(x) = 3(1.18)^x $
2. $ f(x) = 4(1.18)^x $
3. $ f(x) = 4(1.55)^x $
4. $ f(x) = 4(0.66)^x $
5. $ f(x) = 4(0.81)^x $

**Curve Matches:**

- **a. Black (K)**
- **b. Green (G)**
- **c. Red (R)**
- **d. Orange (O)**
- **e. Blue (B)**

**Matching Results:**

- $ f(x) = 3(1.18)^x $ matches with **Orange (O)**
- $ f(x) = 4(1.18)^x $ matches with **Green (G)**
- $ f(x) = 4(1.55)^x $ matches with **Red (R)**
- $ f(x) = 4(0.66)^x $ matches with **Blue (B)**
- $ f(x) = 4(0.81)^x $ matches with **Black (K)**

**Analysis of the Graph:**

- **Red Curve (R):** Rapidly increasing function, indicative of a high growth rate.
- **Orange Curve (O):** Increasing at a slower rate compared to the red curve.
- **Green Curve (G):** Similar behavior to the orange curve, slightly shifted upwards.
- **Blue Curve (B):** Represents a decreasing function, indicating decay.
- **Black Curve (K):** Shows moderate decrease, less steep than the blue curve.

This exercise helps in understanding how exponential functions are represented graphically and how different parameters affect their growth or decay rates.

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