Question

5. The table shows the amount of pet food in cups remaining in an automatic feeder asa function of the number of meals the feeder has dispensed.f(n)= -3n+64Of (n)=1n + 16Automatic FeederAmount of Pet FoodNumber of MealsDispensed, nRemaining, f(n)(cups)121Of (n)= -3n+243156610f(n)-n + 8733Based on the table, which function models this situation?

Answer 1

Given the information on the table, we can find the rate of change of the linear function using the two ordered pair from the table (1,21) and (7,3). Then, we have the following:

`\begin{gathered} \text{ Rate of change:} \\ m=(y_2-y_1)/(x_2-x_1) \end{gathered}`

in this case, we get:

`\begin{gathered} (x_1,y_1)=(1,21) \\ (x_2,y_2)=(7,3) \\ \Rightarrow m=(3-21)/(7-1)=(-18)/(6)=-3 \\ m=-3 \end{gathered}`

now that we have that m = 3, we can use the first ordered pair to find the explicit function using the point-slope formula:

`\begin{gathered} y-y_1=m(x-x_1) \\ \Rightarrow y-21=-3(x-1)=-3x+3 \\ \Rightarrow y=-3x+3+21=-3x+24 \\ y=-3x+24 \end{gathered}`

then, if f(n) = y, the function that models this situation is f(n) = -3n + 24