Based on the table, which function models this situation? a. f(n) = -3n + 24
b. f(n) = -(1/3)n + 16
c. f(n) = -3n + 64
d. f(n) = -(1/3)n + 8

please show how you got the answer!

A is correct.  f(n) = -3n + 24

Step-by-step explanation:

We can see in the first two steps that two meals have been served, and six cups of pet food consumed.  In other words, six cups are consumed in two meals, therefore one cup is consumed in each meal.

If we look at the remaining numbers on the chart, we can see that this carries through.  This tells us that the correct answer must be either a or b, as "-3n" represents the consumption rate.  If it were (1/3)n, then only a third of a cup would be consumed per meal.

Finally, we can figure out which of those two equations is correct simply by plugging a value pair into them.  Starting with a:

f(1) = -3(1) + 24

= 24 - 3

= 21

correct.

To be certain, let's check with answer c:

f(1) = -3(1) + 64

= 64 - 3

= 61

incorrect.

So we can clearly say that the correct answer is "a".  You can plug the other values into it to test that too:

f(3) = -3(3) + 24

= 24 - 9

= 15

correct

So we definitely have the right answer.