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Directions: Circle each function that is an example of exponential decay (there are exactly five of them). Graph each of these decay functions only. 1) f(x) = 2(4)* f(x) = 9-* f(x) = 6( ³ ) * f(x)=3(5)* (1(x) = (²7) 6 (3) = 2* f(x)=6 f(x)=2 211 201 TO 16 17 f(x)=5 f(x)=5 NW

Directions: Circle each function that is an example of exponential decay (there are exactly five of them). Graph each of these decay functions only. 1) f(x) = 2(4)* f(x) = 9-* f(x) = 6( ³ ) * f(x)=3(5)* (1(x) = (²7) 6 (3) = 2* f(x)=6 f(x)=2 211 201 TO 16 17 f(x)=5 f(x)=5 NW

Calculus: Early Transcendentals
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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### Transcription and Explanation for Educational Website #### Problem 3: **Function:** \[ f(x) = \left(\frac{7}{2}\right)^{-x} \] **Table of Values:** | x | y | |----|------------------------| | -2 | \( \left(\frac{7}{2}\right)^{-2} = 12.25 \) | | -1 | \( \left(\frac{7}{2}\right)^{-1} = 3.5 \) | | 0 | \( \left(\frac{7}{2}\right)^{0} = 1 \) | | 1 | \( \left(\frac{7}{2}\right)^{1} = 0.2 \) | | 2 | \( \left(\frac{7}{2}\right)^{2} = 0.8 \) | **Graph Description:** The graph beside the table is a blank grid intended for plotting the function \( f(x) = \left(\frac{7}{2}\right)^{-x} \) as per the values in the table. The x-axis ranges from -3 to 3, and the y-axis from -9 to 9. #### Problem 4: **Function:** \[ f(x) = 2\left(\frac{1}{4}\right)^{-x} \] **Table of Values:** | x | y | |----|-----------------------| | -2 | \( 2\left(\frac{1}{4}\right)^{-2} = 32 \) | | -1 | \( 2\left(\frac{1}{4}\right)^{-1} = 8 \) | | 0 | \( 2\left(\frac{1}{4}\right)^{0} = 2 \) | | 1 | \( 2\left(\frac{1}{4}\right)^{1} = 0.5 \) | | 2 | \( 2\left(\frac{1}{4}\right)^{2} = 0.125 \)| **Graph Description:** The graph beside the table is a blank grid intended for plotting the function \( f(x) = 2\left(\frac{1}{4}\right)
Transcribed Image Text:### Transcription and Explanation for Educational Website #### Problem 3: **Function:** \[ f(x) = \left(\frac{7}{2}\right)^{-x} \] **Table of Values:** | x | y | |----|------------------------| | -2 | \( \left(\frac{7}{2}\right)^{-2} = 12.25 \) | | -1 | \( \left(\frac{7}{2}\right)^{-1} = 3.5 \) | | 0 | \( \left(\frac{7}{2}\right)^{0} = 1 \) | | 1 | \( \left(\frac{7}{2}\right)^{1} = 0.2 \) | | 2 | \( \left(\frac{7}{2}\right)^{2} = 0.8 \) | **Graph Description:** The graph beside the table is a blank grid intended for plotting the function \( f(x) = \left(\frac{7}{2}\right)^{-x} \) as per the values in the table. The x-axis ranges from -3 to 3, and the y-axis from -9 to 9. #### Problem 4: **Function:** \[ f(x) = 2\left(\frac{1}{4}\right)^{-x} \] **Table of Values:** | x | y | |----|-----------------------| | -2 | \( 2\left(\frac{1}{4}\right)^{-2} = 32 \) | | -1 | \( 2\left(\frac{1}{4}\right)^{-1} = 8 \) | | 0 | \( 2\left(\frac{1}{4}\right)^{0} = 2 \) | | 1 | \( 2\left(\frac{1}{4}\right)^{1} = 0.5 \) | | 2 | \( 2\left(\frac{1}{4}\right)^{2} = 0.125 \)| **Graph Description:** The graph beside the table is a blank grid intended for plotting the function \( f(x) = 2\left(\frac{1}{4}\right)
**Directions:** Circle each function that is an example of exponential decay (there are exactly five of them). Graph each of these decay functions only. Functions provided: 1. \( f(x) = 2 \left(4\right)^x \) 2. \( f(x) = 3 \left(5\right)^x \) 3. \( f(x) = 6 \left(\frac{2}{3}\right)^x \) 4. \( f(x) = 5 \left(\frac{3}{2}\right)^x \) 5. \( f(x) = 9^{-x} \) 6. \( f(x) = \left(\frac{7}{2}\right)^{-x} \) 7. \( f(x) = 2 \left(\frac{1}{4}\right)^x \) 8. \( f(x) = 5 \left(\frac{3}{7}\right)^x \) Circled functions indicating exponential decay: - \( f(x) = 6 \left(\frac{2}{3}\right)^x \) - \( f(x) = 5 \left(\frac{3}{2}\right)^{-x} \) - \( f(x) = 9^{-x} \) - \( f(x) = \left(\frac{7}{2}\right)^{-x} \) - \( f(x) = 2 \left(\frac{1}{4}\right)^x \) **1) Function: \( f(x) = 6 \left(\frac{2}{3}\right)^x \)** | x | \( y \) | |----|-----------------------------| | -2 | \( 6 \left(\frac{2}{3}\right)^{-2} = 13.5 \) | | -1 | \( 6 \left(\frac{2}{3}\right)^{-1} = 9 \) | | 0 | \( 6 \left(\frac{2}{3}\right)^0 = 6 \) | | 1 | \( 6 \left(\frac{2}{3}\right)^1 = 4 \) | | 2 | \( 6 \left(\frac{2}{3}\right)^2 = 2.6 \) | - **Graph Description:**
Transcribed Image Text:**Directions:** Circle each function that is an example of exponential decay (there are exactly five of them). Graph each of these decay functions only. Functions provided: 1. \( f(x) = 2 \left(4\right)^x \) 2. \( f(x) = 3 \left(5\right)^x \) 3. \( f(x) = 6 \left(\frac{2}{3}\right)^x \) 4. \( f(x) = 5 \left(\frac{3}{2}\right)^x \) 5. \( f(x) = 9^{-x} \) 6. \( f(x) = \left(\frac{7}{2}\right)^{-x} \) 7. \( f(x) = 2 \left(\frac{1}{4}\right)^x \) 8. \( f(x) = 5 \left(\frac{3}{7}\right)^x \) Circled functions indicating exponential decay: - \( f(x) = 6 \left(\frac{2}{3}\right)^x \) - \( f(x) = 5 \left(\frac{3}{2}\right)^{-x} \) - \( f(x) = 9^{-x} \) - \( f(x) = \left(\frac{7}{2}\right)^{-x} \) - \( f(x) = 2 \left(\frac{1}{4}\right)^x \) **1) Function: \( f(x) = 6 \left(\frac{2}{3}\right)^x \)** | x | \( y \) | |----|-----------------------------| | -2 | \( 6 \left(\frac{2}{3}\right)^{-2} = 13.5 \) | | -1 | \( 6 \left(\frac{2}{3}\right)^{-1} = 9 \) | | 0 | \( 6 \left(\frac{2}{3}\right)^0 = 6 \) | | 1 | \( 6 \left(\frac{2}{3}\right)^1 = 4 \) | | 2 | \( 6 \left(\frac{2}{3}\right)^2 = 2.6 \) | - **Graph Description:**
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As per the instruction, we will be answering the first three subparts.

For (a),

Calculus homework question answer, step 1, image 1

Graph:

Calculus homework question answer, step 1, image 2

For (b),

Calculus homework question answer, step 1, image 3

Graph:

Calculus homework question answer, step 1, image 4

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