20 y=16.00 10 x2.00 2 Drag the purple X on the horizontal axis to vary value of x. The value of x and the corresponding value of y are shown on their respective axes. a. Use the applet above to approximate the value of x such that 4* 37. Preview b. Check your answer to part (a) by entering "4^#" into the answer entry box below and looking at the preview value. The result should be close to 37. Preview c. We can estimate solutions to equations like 4* = 2000 by thinking about the two integer values that the answer must be between. For example, the solution to 4" = 2000 must be greater than and less than because 45 1024 and 46 4096. 4.
20 y=16.00 10 x2.00 2 Drag the purple X on the horizontal axis to vary value of x. The value of x and the corresponding value of y are shown on their respective axes. a. Use the applet above to approximate the value of x such that 4* 37. Preview b. Check your answer to part (a) by entering "4^#" into the answer entry box below and looking at the preview value. The result should be close to 37. Preview c. We can estimate solutions to equations like 4* = 2000 by thinking about the two integer values that the answer must be between. For example, the solution to 4" = 2000 must be greater than and less than because 45 1024 and 46 4096. 4.
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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![The following applet shows the graph of \( f(x) = 4^x \), where \( y = f(x) \). Use the applet to vary the value of \( x \) and pay attention to the output value.
**Graph Description:**
- The graph displays the exponential function \( y = 4^x \).
- The vertical y-axis ranges from 0 to 40.
- The horizontal x-axis ranges from 0 to 4.
- A point on the graph indicates \( y \approx 16.00 \) when \( x \approx 2.00 \).
- A purple 'X' on the horizontal axis can be dragged to vary the value of \( x \).
- The graph assists in visually understanding the relationship between \( x \) and \( y \).
**Instructions:**
a. Use the applet above to approximate the value of \( x \) such that \( 4^x = 37 \).
\( x \approx \) [Input Box] [Preview Button]
b. Check your answer to part (a) by entering "4^#" into the answer entry box below and looking at the preview value. The result should be close to 37.
[Preview Button]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcbb2b57d-b82b-4c44-a3ed-52ccdcaab288%2F6a873f75-3260-4a5c-89ec-26affa764435%2Fvxwg4ve_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The following applet shows the graph of \( f(x) = 4^x \), where \( y = f(x) \). Use the applet to vary the value of \( x \) and pay attention to the output value.
**Graph Description:**
- The graph displays the exponential function \( y = 4^x \).
- The vertical y-axis ranges from 0 to 40.
- The horizontal x-axis ranges from 0 to 4.
- A point on the graph indicates \( y \approx 16.00 \) when \( x \approx 2.00 \).
- A purple 'X' on the horizontal axis can be dragged to vary the value of \( x \).
- The graph assists in visually understanding the relationship between \( x \) and \( y \).
**Instructions:**
a. Use the applet above to approximate the value of \( x \) such that \( 4^x = 37 \).
\( x \approx \) [Input Box] [Preview Button]
b. Check your answer to part (a) by entering "4^#" into the answer entry box below and looking at the preview value. The result should be close to 37.
[Preview Button]
![The image contains a graph and instructions related to finding values of \(x\) for exponential equations.
### Graph Explanation:
- The graph shows an exponential curve representing \(y = 4^x\).
- A purple "X" is marked on the horizontal axis at \(x \approx 2.00\).
- There is a dashed vertical line from the "X" to the curve, intersecting at a point where \(y \approx 16.00\).
### Text Instructions:
1. **Interactive Applet Instruction:**
- "Drag the purple X on the horizontal axis to vary the value of \(x\). The value of \(x\) and the corresponding value of \(y\) are shown on their respective axes."
2. **Task A:**
- "Use the applet above to approximate the value of \(x\) such that \(4^x = 37\)."
- An input box for \(x \approx\) with a "Preview" button.
3. **Task B:**
- "Check your answer to part (a) by entering '4^#' into the answer entry box below and looking at the preview value. The result should be close to 37."
- An entry box with a "Preview" button.
4. **Task C:**
- "We can estimate solutions to equations like \(4^x = 2000\) by thinking about the two integer values that the answer must be between. For example, the solution to \(4^x = 2000\) must be greater than [___] and less than [___] because \(4^5 = 1024\) and \(4^6 = 4096\)."
In task C, users are prompted to fill in the blanks with integer values indicating the range for the solution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcbb2b57d-b82b-4c44-a3ed-52ccdcaab288%2F6a873f75-3260-4a5c-89ec-26affa764435%2Fkziihz_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image contains a graph and instructions related to finding values of \(x\) for exponential equations.
### Graph Explanation:
- The graph shows an exponential curve representing \(y = 4^x\).
- A purple "X" is marked on the horizontal axis at \(x \approx 2.00\).
- There is a dashed vertical line from the "X" to the curve, intersecting at a point where \(y \approx 16.00\).
### Text Instructions:
1. **Interactive Applet Instruction:**
- "Drag the purple X on the horizontal axis to vary the value of \(x\). The value of \(x\) and the corresponding value of \(y\) are shown on their respective axes."
2. **Task A:**
- "Use the applet above to approximate the value of \(x\) such that \(4^x = 37\)."
- An input box for \(x \approx\) with a "Preview" button.
3. **Task B:**
- "Check your answer to part (a) by entering '4^#' into the answer entry box below and looking at the preview value. The result should be close to 37."
- An entry box with a "Preview" button.
4. **Task C:**
- "We can estimate solutions to equations like \(4^x = 2000\) by thinking about the two integer values that the answer must be between. For example, the solution to \(4^x = 2000\) must be greater than [___] and less than [___] because \(4^5 = 1024\) and \(4^6 = 4096\)."
In task C, users are prompted to fill in the blanks with integer values indicating the range for the solution.
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