Answer :
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:
[tex]\begin{gathered} \text{ Rate of change:} \\ m=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]in this case, we get:
[tex]\begin{gathered} (x_1,y_1)=(1,21) \\ (x_2,y_2)=(7,3) \\ \Rightarrow m=\frac{3-21}{7-1}=\frac{-18}{6}=-3 \\ m=-3 \end{gathered}[/tex]now that we have that m = 3, we can use the first ordered pair to find the explicit function using the point-slope formula:
[tex]\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}[/tex]then, if f(n) = y, the function that models this situation is f(n) = -3n + 24
