Question

The number of bacteria in a certain food is a function of the food’s temperature. The number is N1(T) at a temperature T degrees Celsius, described by the equation N1(T) = 15T2 + 60T + 300. Similarly, the number of bacteria in another food is given by the function, N2(T) = 20T2 – 5T + 150. Determine an equation that describes the number of bacteria in both the foods when they are mixed.30T2 + 55T + 45035T2 + 65T + 45035T2 + 55T + 450- 5T2 - 65T + 150

Answer 1

If we mix the two foods together, then we need to add the two equations to get the total number of bacteria. We are given the two equations:

`\begin{gathered} N_1(T)=15T^2+60T+300 \\ N_2(T)=20T^2-5T+150 \end{gathered}`

Thus, we add:

`N_3(T)=N_1(T)+N_2(T)=(15T^2+60T+300)+(20T^2-5T+150)=35T^2+55T+450`

Thus, the correct answer is the third option:

`35T^2+55T+450`