The number of bacteria in a refrigerated food product is given by N(T) = 26T2 - 117T +27,5 < T < 35 where I' 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. Find the composite function N(T(t)): N(T(t)) = - Find the time when the bacteria count reaches 9615. Give your answer accurate to at least 2 decimal places. Time Needed = hours

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.
Chapter3: The Derivative
Section3.4: Definition Of The Derivative
Problem 50E
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### Bacteria Growth in Refrigerated Food

The number of bacteria in a refrigerated food product is determined by the function:

\[ N(T) = 26T^2 - 117T + 27, \quad 5 < T < 35 \]

where \( T \) represents the temperature of the food.

When this food is removed from the refrigerator, the change in temperature over time is described by the function:

\[ T(t) = 3t + 1.4 \]

where \( t \) is the time in hours.

**Task 1: Find the Composite Function \( N(T(t)) \)**

\[ N(T(t)) = \]

**Task 2: Determine the Time When Bacteria Count Reaches 9615**

Find the time required for the number of bacteria to reach 9615. Provide your answer with at least two decimal places.

**Time Needed:** 

\[ \text{Time Needed} = \quad \text{hours} \]
Transcribed Image Text:### Bacteria Growth in Refrigerated Food The number of bacteria in a refrigerated food product is determined by the function: \[ N(T) = 26T^2 - 117T + 27, \quad 5 < T < 35 \] where \( T \) represents the temperature of the food. When this food is removed from the refrigerator, the change in temperature over time is described by the function: \[ T(t) = 3t + 1.4 \] where \( t \) is the time in hours. **Task 1: Find the Composite Function \( N(T(t)) \)** \[ N(T(t)) = \] **Task 2: Determine the Time When Bacteria Count Reaches 9615** Find the time required for the number of bacteria to reach 9615. Provide your answer with at least two decimal places. **Time Needed:** \[ \text{Time Needed} = \quad \text{hours} \]
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