Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.3: Maxima And Minima
Problem 19E
Related questions
Question
![**Composite Function and Bacteria Growth Problem**
The number of bacteria in a refrigerated food product is given by:
\[ N(T) = 26T^2 - 117T + 27, \quad 5 < T < 35 \]
where \( T \) is the temperature of the food.
When the food is removed from the refrigerator, the temperature is given by:
\[ T(t) = 3t + 1.4 \]
where \( t \) is the time in hours.
**Tasks:**
1. **Find the composite function \( N(T(t)) \):**
\[ N(T(t)) = \]
2. **Calculate the time when the bacteria count reaches 9615.** Give your answer accurate to at least 2 decimal places.
\[ \text{Time Needed} = \quad \text{hours} \]
**Supporting Information:**
- Video assistance is available for this problem. Click on the video link for a step-by-step explanation.
**Graphical Explanation:**
No graphs or diagrams are given in the problem statement. For visualization, consider plotting the functions \( N(T) \) and \( T(t) \) onto a graph for better understanding. \( N(T) \) is a quadratic function depicting the growth of bacteria concerning temperature, and \( T(t) \) is a linear function depicting the increase in temperature over time.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa78a88d7-60f0-4b9e-a272-6ff852667c68%2F145fc18e-1150-4c58-8e4a-c2362d510563%2Fewbbta_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Composite Function and Bacteria Growth Problem**
The number of bacteria in a refrigerated food product is given by:
\[ N(T) = 26T^2 - 117T + 27, \quad 5 < T < 35 \]
where \( T \) is the temperature of the food.
When the food is removed from the refrigerator, the temperature is given by:
\[ T(t) = 3t + 1.4 \]
where \( t \) is the time in hours.
**Tasks:**
1. **Find the composite function \( N(T(t)) \):**
\[ N(T(t)) = \]
2. **Calculate the time when the bacteria count reaches 9615.** Give your answer accurate to at least 2 decimal places.
\[ \text{Time Needed} = \quad \text{hours} \]
**Supporting Information:**
- Video assistance is available for this problem. Click on the video link for a step-by-step explanation.
**Graphical Explanation:**
No graphs or diagrams are given in the problem statement. For visualization, consider plotting the functions \( N(T) \) and \( T(t) \) onto a graph for better understanding. \( N(T) \) is a quadratic function depicting the growth of bacteria concerning temperature, and \( T(t) \) is a linear function depicting the increase in temperature over time.
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