4. Assume that each variable of the function in y is a function of time t. Desmos | Graphing Calculator https://www.desmos.com/calculator Car 1 starts on the graph of y = e^x at the point (0,1) and car 2 starts on the graph of Y = 3x-2 at the point (0,-2) y= e* and distance is measured in miles. If both cars start moving to the right at the same time in such a way that Sx =D1 St y= 3x-2 |(0,1) mile/minute, -05 (g-2) at what rate is the distance between the cars changing when t= 3 minutes? (You may assume that the vertical and the shortest distances are identical.)
4. Assume that each variable of the function in y is a function of time t. Desmos | Graphing Calculator https://www.desmos.com/calculator Car 1 starts on the graph of y = e^x at the point (0,1) and car 2 starts on the graph of Y = 3x-2 at the point (0,-2) y= e* and distance is measured in miles. If both cars start moving to the right at the same time in such a way that Sx =D1 St y= 3x-2 |(0,1) mile/minute, -05 (g-2) at what rate is the distance between the cars changing when t= 3 minutes? (You may assume that the vertical and the shortest distances are identical.)
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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![**Title: Analyzing the Rates of Change in Function-Based Movement**
---
**Problem Statement:**
4. Assume that each variable of the function in \( y \) is a function of time \( t \).
**Graph Description:**
The graph displays two functions:
- \( y = e^x \), an exponential curve.
- \( y = 3x - 2 \), a straight line with a slope of 3.
Each function has a distinct starting point:
- The curve \( y = e^x \) passes through the point \((0, 1)\).
- The line \( y = 3x - 2 \) passes through the point \((0, -2)\).
**Scenario:**
- Car 1 starts on the graph of \( y = e^x \) at the point \((0, 1)\).
- Car 2 starts on the graph of \( y = 3x - 2 \) at the point \((0, -2)\).
- Distances are measured in miles.
Both cars move to the right simultaneously with a speed governed by:
\[
\frac{\delta x}{\delta t} = 1 \text{ mile/minute}
\]
**Question:**
At what rate is the distance between the cars changing when \( t = 3 \) minutes?
*(You may assume that the vertical and the shortest distances are identical.)*
**Explanation:**
This problem involves calculating the rate at which the distance between two dynamically moving points, represented by cars, is changing as time passes. The cars follow their respective paths: an exponential curve and a linear path. This involves a conceptual understanding of derivatives and rate of change in coordinate geometry.
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F62c6665b-9dd6-42c0-b1e6-31e46db0a556%2F9d1c40fb-21c7-47af-bacb-11e76cbe2aa7%2F7d1ok5_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Analyzing the Rates of Change in Function-Based Movement**
---
**Problem Statement:**
4. Assume that each variable of the function in \( y \) is a function of time \( t \).
**Graph Description:**
The graph displays two functions:
- \( y = e^x \), an exponential curve.
- \( y = 3x - 2 \), a straight line with a slope of 3.
Each function has a distinct starting point:
- The curve \( y = e^x \) passes through the point \((0, 1)\).
- The line \( y = 3x - 2 \) passes through the point \((0, -2)\).
**Scenario:**
- Car 1 starts on the graph of \( y = e^x \) at the point \((0, 1)\).
- Car 2 starts on the graph of \( y = 3x - 2 \) at the point \((0, -2)\).
- Distances are measured in miles.
Both cars move to the right simultaneously with a speed governed by:
\[
\frac{\delta x}{\delta t} = 1 \text{ mile/minute}
\]
**Question:**
At what rate is the distance between the cars changing when \( t = 3 \) minutes?
*(You may assume that the vertical and the shortest distances are identical.)*
**Explanation:**
This problem involves calculating the rate at which the distance between two dynamically moving points, represented by cars, is changing as time passes. The cars follow their respective paths: an exponential curve and a linear path. This involves a conceptual understanding of derivatives and rate of change in coordinate geometry.
---
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