The number of bacteria in a refrigerated food product is given by N(T) = 23T² – 96T + 12, 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) = 5t + 1.5, where t is the time in hours. Find the composite function N(T(t)): N(T(t)) = Find the number of bacteria after 6.2 hours. Give your answer accurate to the nearest whole value. bacteria
The number of bacteria in a refrigerated food product is given by N(T) = 23T² – 96T + 12, 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) = 5t + 1.5, where t is the time in hours. Find the composite function N(T(t)): N(T(t)) = Find the number of bacteria after 6.2 hours. Give your answer accurate to the nearest whole value. bacteria
Chapter2: Functions And Their Graphs
Section2.4: A Library Of Parent Functions
Problem 47E: During a nine-hour snowstorm, it snows at a rate of 1 inch per hour for the first 2 hours, at a rate...
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![### Understanding Bacterial Growth in Refrigerated Food
The number of bacteria in a refrigerated food product can be described using the function:
\[ N(T) = 23T^2 - 96T + 12 \]
where \( T \) is the temperature of the food measured in degrees Celsius (°C), and the temperature range is \( 5 < T < 35 \).
When the food is removed from the refrigerator, the temperature increases over time and is given by the function:
\[ T(t) = 5t + 1.5 \]
where \( t \) is the time in hours after the food is taken out.
### Finding the Composite Function \( N(T(t)) \)
To find the composite function \( N(T(t)) \), we need to substitute the expression for \( T(t) \) into the function \( N(T) \):
\[ N(T(t)) = \]
### Determining Bacterial Count After 6.2 Hours
To find the number of bacteria after 6.2 hours, substitute \( t = 6.2 \) into the composite function \( N(T(t)) \) and compute the result. Ensure your answer is accurate to the nearest whole number.
\[
\text{Number of bacteria} = \quad \text{bacteria}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F90d1e96e-989a-4849-aeb9-585c1e797a4d%2Fbfca44d7-4268-4707-b7b2-cc2b4f5c9f9c%2Fk7r1by6_processed.png&w=3840&q=75)
Transcribed Image Text:### Understanding Bacterial Growth in Refrigerated Food
The number of bacteria in a refrigerated food product can be described using the function:
\[ N(T) = 23T^2 - 96T + 12 \]
where \( T \) is the temperature of the food measured in degrees Celsius (°C), and the temperature range is \( 5 < T < 35 \).
When the food is removed from the refrigerator, the temperature increases over time and is given by the function:
\[ T(t) = 5t + 1.5 \]
where \( t \) is the time in hours after the food is taken out.
### Finding the Composite Function \( N(T(t)) \)
To find the composite function \( N(T(t)) \), we need to substitute the expression for \( T(t) \) into the function \( N(T) \):
\[ N(T(t)) = \]
### Determining Bacterial Count After 6.2 Hours
To find the number of bacteria after 6.2 hours, substitute \( t = 6.2 \) into the composite function \( N(T(t)) \) and compute the result. Ensure your answer is accurate to the nearest whole number.
\[
\text{Number of bacteria} = \quad \text{bacteria}
\]
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