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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Question 38
![### Text Transcription for Educational Use
**Example 10: Environmental Study and Pollution Levels**
In Example 10, it was observed through an environmental study of a certain suburban community, that there is a relationship between the population level \( p \) (in thousands) and the amount of carbon monoxide \( C \) (in ppm) in the air. The relationship is defined as:
\[ C(p) = \sqrt{0.5p^2 + 17} \]
Assuming the population \( p \) (in thousands) at time \( t \) is modeled by the function:
\[ p(t) = 0.1062e^{0.023t} \]
Use the chain rule to find the rate at which the pollution level is changing after three years and compare this with the estimate obtained in Example 10.
**Figure 3.19: Average Height as a Function of Age**
This figure shows the average height of boys and girls in the United States as a function of age, expressed in months. This relationship is described by the linear function:
\[ h(t) = 32 + 0.19t \, \text{inches} \]
- **Graph Analysis: Boys and Girls Heights**
- **Boys**: The graph shows height on the y-axis (in inches) against age in months on the x-axis. The points form a nearly straight line, indicating a steady growth rate.
- **Girls**: Similarly, the graph for girls demonstrates height on the y-axis and age in months on the x-axis. The linear trend is consistent with boys, indicating a similar growth pattern.
This information helps in understanding growth patterns and environmental impacts related to population changes.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe4db1e84-75df-498d-9686-5cabfd0e0c2f%2F917cccac-796b-4717-88ef-c7de9377a273%2Fccdx0qw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Text Transcription for Educational Use
**Example 10: Environmental Study and Pollution Levels**
In Example 10, it was observed through an environmental study of a certain suburban community, that there is a relationship between the population level \( p \) (in thousands) and the amount of carbon monoxide \( C \) (in ppm) in the air. The relationship is defined as:
\[ C(p) = \sqrt{0.5p^2 + 17} \]
Assuming the population \( p \) (in thousands) at time \( t \) is modeled by the function:
\[ p(t) = 0.1062e^{0.023t} \]
Use the chain rule to find the rate at which the pollution level is changing after three years and compare this with the estimate obtained in Example 10.
**Figure 3.19: Average Height as a Function of Age**
This figure shows the average height of boys and girls in the United States as a function of age, expressed in months. This relationship is described by the linear function:
\[ h(t) = 32 + 0.19t \, \text{inches} \]
- **Graph Analysis: Boys and Girls Heights**
- **Boys**: The graph shows height on the y-axis (in inches) against age in months on the x-axis. The points form a nearly straight line, indicating a steady growth rate.
- **Girls**: Similarly, the graph for girls demonstrates height on the y-axis and age in months on the x-axis. The linear trend is consistent with boys, indicating a similar growth pattern.
This information helps in understanding growth patterns and environmental impacts related to population changes.
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