The number of bacteria in a refrigerated food product is given by N(T) = 24T2 - 109T+82, 4 < T < 34 where I is the temperature of the food. When the food is removed from the refrigerator, the temperature is given by T(t) = 4t+1.5, 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 11040. Give your answer accurate to at least 2 decimal places. Time Needed = hours
The number of bacteria in a refrigerated food product is given by N(T) = 24T2 - 109T+82, 4 < T < 34 where I is the temperature of the food. When the food is removed from the refrigerator, the temperature is given by T(t) = 4t+1.5, 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 11040. Give your answer accurate to at least 2 decimal places. Time Needed = hours
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter4: Exponential And Logarithmic Functions
Section: Chapter Questions
Problem 3CC: If xis large, which function grows faster, f(x)=2x or g(x)=x2?
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Question
![The number of bacteria in a refrigerated food product is given by \( N(T) = 24T^2 - 109T + 82, \quad 4 < T < 34 \) where \( T \) is the temperature of the food.
When the food is removed from the refrigerator, the temperature is given by:
\[ T(t) = 4t + 1.5, \]
where \( t \) is the time in hours.
### Tasks
1. Find the composite function \(N(T(t))\):
\[ N(T(t)) = \]
2. Find the time when the bacteria count reaches 11040. Give your answer accurate to at least 2 decimal places.
\[ \text{Time Needed} = \] hours](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa78a88d7-60f0-4b9e-a272-6ff852667c68%2Fab69e432-935d-4a46-b346-34c6ed9e049c%2Fk3phv4t_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The number of bacteria in a refrigerated food product is given by \( N(T) = 24T^2 - 109T + 82, \quad 4 < T < 34 \) where \( T \) is the temperature of the food.
When the food is removed from the refrigerator, the temperature is given by:
\[ T(t) = 4t + 1.5, \]
where \( t \) is the time in hours.
### Tasks
1. Find the composite function \(N(T(t))\):
\[ N(T(t)) = \]
2. Find the time when the bacteria count reaches 11040. Give your answer accurate to at least 2 decimal places.
\[ \text{Time Needed} = \] hours
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