The log of the field metabolic rate (FMR) or the log of the total energy expenditure per day in excess of growth is calculated for pronghorm fawns using Nagy's formula E(x) = 0.774 +0.716 ln(x), where x is the mass of the fawn (in g) and E(x) is the log of the energy expenditure (in kJ/day). a. Compute the derivative E'(x). E'(x) = kJ/day/day. b. Find the log of the energy expenditure when x = 13000, E(13000) = kJ/day. Compute E' (13000). E' (13000): = kJ/day/day.
The log of the field metabolic rate (FMR) or the log of the total energy expenditure per day in excess of growth is calculated for pronghorm fawns using Nagy's formula E(x) = 0.774 +0.716 ln(x), where x is the mass of the fawn (in g) and E(x) is the log of the energy expenditure (in kJ/day). a. Compute the derivative E'(x). E'(x) = kJ/day/day. b. Find the log of the energy expenditure when x = 13000, E(13000) = kJ/day. Compute E' (13000). E' (13000): = kJ/day/day.
Calculus: Early Transcendentals
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Chapter1: Functions And Models
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![**Understanding Field Metabolic Rate (FMR) in Pronghorn Fawns**
The log of the field metabolic rate (FMR), or the log of the total energy expenditure per day in excess of growth, is calculated for pronghorn fawns using Nagy's formula:
\[ E(x) = 0.774 + 0.716 \ln(x), \]
where \( x \) is the mass of the fawn (in grams), and \( E(x) \) represents the log of the energy expenditure (in kJ/day).
### Tasks:
**a. Compute the Derivative \( E'(x) \).**
\[ E'(x) = \] __________ kJ/day/day.
**b. Find the Log of the Energy Expenditure When \( x = 13000 \).**
\[ E(13000) = \] __________ kJ/day.
Compute:
\[ E'(13000) = \] __________ kJ/day/day.
**Considerations:**
Reflect on the biological interpretation of these results and create a sketch of the graph of the function to better understand the relationship between the mass of the fawn and its energy expenditure.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8afd835b-b164-4187-8cbf-01a7fb9b88d5%2F40bffc15-2502-4103-a979-0fbd47a43c10%2Ftectxm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding Field Metabolic Rate (FMR) in Pronghorn Fawns**
The log of the field metabolic rate (FMR), or the log of the total energy expenditure per day in excess of growth, is calculated for pronghorn fawns using Nagy's formula:
\[ E(x) = 0.774 + 0.716 \ln(x), \]
where \( x \) is the mass of the fawn (in grams), and \( E(x) \) represents the log of the energy expenditure (in kJ/day).
### Tasks:
**a. Compute the Derivative \( E'(x) \).**
\[ E'(x) = \] __________ kJ/day/day.
**b. Find the Log of the Energy Expenditure When \( x = 13000 \).**
\[ E(13000) = \] __________ kJ/day.
Compute:
\[ E'(13000) = \] __________ kJ/day/day.
**Considerations:**
Reflect on the biological interpretation of these results and create a sketch of the graph of the function to better understand the relationship between the mass of the fawn and its energy expenditure.
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