Answer :
Final Answer:
The given sattement "The number of bacteria in a refrigerated food product is given by T(t) =3t+1.3tN(T(t) ) =N(T) =24T2−108T+97.4, where T is the temperature of the food. When the food is removed from the refrigeration" is fasle because when the food is removed from refrigeration, the temperature will start increasing, resulting in a change in the number of bacteria. So, the correct option is b) False.
Explanation:
Given the function T(t) = 3t + 1.3tN(T(t)) = 24T^2 - 108T + 97.4, it is clear that the number of bacteria in the food product is dependent on both time (t) and temperature (T). When the food is removed from refrigeration, the temperature will start increasing, resulting in a change in the number of bacteria.
The given equation T(t) = 3t + 1.3tN(T(t)) = 24T^2 - 108T + 97.4 represents the relationship between time and temperature, and the number of bacteria in the food product, respectively. Since T is dependent on time, removing the food from refrigeration will lead to an increase in temperature over time.
To determine the impact on the number of bacteria, we need to evaluate the function N(T(t)) after the food is removed from refrigeration. As time progresses and temperature rises, the number of bacteria will change accordingly.
The function N(T(t)) = 24[tex]T^2[/tex]- 108T + 97.4 shows that the number of bacteria is a quadratic function of temperature. As the temperature increases, the number of bacteria will follow this quadratic relationship.
Thus, based on the given information, we can conclude that when the food is removed from refrigeration, the number of bacteria will change, making the statement "False."
So, the correct option is b) False.
