Suppose that the number of bacteria in a plate of food is given by N(T)= 10T^2 - 40T + 200, -1<=T<=20
where T is the temperature of the food in degrees Celsius. Suppose that the temperature of the food when it is left out on a picnic table is given by T(t)= 4t + 10, 0<=t<=2
where t is the time in hours.
I solved the other parts to this question, but not sure about this: What is the physical interpretation of this composition function? N(T(t))
Since T(t) is the temperature after t hours,
N(T(t)) is the number of bacteria after t hours
The composition function N(T(t)) represents the number of bacteria in the plate of food at a specific time, taking into account the temperature of the food at that time.
To compute N(T(t)), we first need to substitute the expression for T(t) into the equation N(T). In this case, the temperature T(t) is given by 4t + 10. Therefore, we can substitute T(t) = 4t + 10 into the equation N(T), which gives us:
N(T(t)) = 10(4t + 10)^2 - 40(4t + 10) + 200
Simplifying this expression will give us a function that represents the number of bacteria in the plate of food as a function of time t.
The physical interpretation of this composition function is that it allows us to analyze how the number of bacteria in the food changes over time, while taking into account the corresponding temperature changes. By substituting different values of t into the function N(T(t)), we can determine the number of bacteria at different points in time based on the temperature of the food at those times.
So, the composition function N(T(t)) provides a mathematical model that can help us understand the relationship between temperature and bacterial growth in the food over a certain time period.