Question

Number of meals dispensed, n | amount of pet food left, f(n) (cups)
1 | 21
3 | 15
6 | 6
7 | 3

The table shows the amount of pet food in cups remaining in an automatic feeder as a function of the number of meals the feeder has dispensed.

what function models this situation?

f(x) = ?

Answer 1

Find the slope: between points the change in food per meal is constant:
(15−21)/(3−1)=−6/2=−3, and similarly for other pairs. So f is linear with slope −3.

Use a point to get intercept: 21 = −3(1) + b ⇒ b = 24.

Thus f(x) = 24 − 3x.