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
The rate (in mg carbon/m3/h) at which photosynthesis takes place for a species of phytoplankton is modeled by the function where I is the light intensity (measured in thousands of foot-candles). For what light intensity is P a maximum?
![The image shows a mathematical equation for power \( P \) as a function of current \( I \):
\[
P = \frac{80I}{I^2 + I + 9}
\]
In this equation:
- \( P \) represents the power.
- \( I \) is the current.
- The numerator \( 80I \) implies that power is directly proportional to the current, scaled by a factor of 80.
- The denominator \( I^2 + I + 9 \) is a quadratic expression that affects how the power changes with current.
This type of equation can be used to analyze the relationship between power and current in electrical circuits, showing how power output varies based on changes in current flow.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F720d6eb4-3e74-4c07-9c9e-1ec6f752b7ac%2F6efb707f-4477-40b4-a634-b5cd4a0858b4%2Fd1onogp_processed.png&w=3840&q=75)
Transcribed Image Text:The image shows a mathematical equation for power \( P \) as a function of current \( I \):
\[
P = \frac{80I}{I^2 + I + 9}
\]
In this equation:
- \( P \) represents the power.
- \( I \) is the current.
- The numerator \( 80I \) implies that power is directly proportional to the current, scaled by a factor of 80.
- The denominator \( I^2 + I + 9 \) is a quadratic expression that affects how the power changes with current.
This type of equation can be used to analyze the relationship between power and current in electrical circuits, showing how power output varies based on changes in current flow.
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