The following equation calculates the number of years y it takes for x percent of the robin population to die. See attached Estimate analytically the percentage of robins that died after 4 years. Do not round until final answer, then round to 4 decimal spaces if needed.
The following equation calculates the number of years y it takes for x percent of the robin population to die. See attached Estimate analytically the percentage of robins that died after 4 years. Do not round until final answer, then round to 4 decimal spaces if needed.
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 equation calculates the number of years y it takes for x percent of the robin population to die. See attached
Estimate analytically the percentage of robins that died after 4 years. Do not round until final answer, then round to 4 decimal spaces if needed.
![### Title: Understanding Logarithmic Equations
#### Subject: Robins
The equation provided is:
\[
y = \frac{3 - \log(100-x)}{0.42}
\]
**Explanation:**
- **Variable \(y\):** Represents the output or dependent variable of the equation.
- **Logarithm (\(\log\)):** The function \(\log(100-x)\) is the logarithm of the expression \(100-x\). Logarithms are the inverse operation of exponentiation and are essential in scenarios where the rate of change of a quantity is dependent on its current value.
- **Expression \(100-x\):** This is the argument of the logarithmic function. The variable \(x\) should be less than 100 for this log function to be defined under real numbers.
- **Multiplier 3:** It appears as a constant in the expression \(3 - \log(100-x)\), adjusting the scale or shift of the logarithmic output.
- **Divisor \(0.42\):** This constant term divides the entire expression, scaling the output value \(y\).
**Applications:**
Logarithmic equations like this one are useful in various fields such as biology, economics, and physics, where they model processes or behaviors like growth rates, decay, and intensities.
**Note:**
Care should be taken when defining the domain of this function. Since it's logarithmic, the input expression \(100-x\) must be greater than zero. Thus, \(x\) should be less than 100 for the function to remain within the domain of real numbers.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3fa757ec-9ef0-41e2-a2d2-ee98e8402c6d%2F275e2478-276c-4890-926b-024a0381f23d%2Fn6zuf8d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Title: Understanding Logarithmic Equations
#### Subject: Robins
The equation provided is:
\[
y = \frac{3 - \log(100-x)}{0.42}
\]
**Explanation:**
- **Variable \(y\):** Represents the output or dependent variable of the equation.
- **Logarithm (\(\log\)):** The function \(\log(100-x)\) is the logarithm of the expression \(100-x\). Logarithms are the inverse operation of exponentiation and are essential in scenarios where the rate of change of a quantity is dependent on its current value.
- **Expression \(100-x\):** This is the argument of the logarithmic function. The variable \(x\) should be less than 100 for this log function to be defined under real numbers.
- **Multiplier 3:** It appears as a constant in the expression \(3 - \log(100-x)\), adjusting the scale or shift of the logarithmic output.
- **Divisor \(0.42\):** This constant term divides the entire expression, scaling the output value \(y\).
**Applications:**
Logarithmic equations like this one are useful in various fields such as biology, economics, and physics, where they model processes or behaviors like growth rates, decay, and intensities.
**Note:**
Care should be taken when defining the domain of this function. Since it's logarithmic, the input expression \(100-x\) must be greater than zero. Thus, \(x\) should be less than 100 for the function to remain within the domain of real numbers.
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