Question

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!

Answer 1

A is correct. f(n) = -3n + 24

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 three cups are 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.

Answer 2

The function that best models the given situation is c. f(n) = -3n + 64.

To determine which function models the situation, we need to check if any of the given options consistently match the values in the table.

Let's analyze each option:

a. f(n) = -3n + 24:

When n = 1, f(n) = -3(1) + 24 = 21 (matches the table)

When n = 3, f(n) = -3(3) + 24 = 15 (matches the table)

When n = 6, f(n) = -3(6) + 24 = 6 (matches the table)

When n = 7, f(n) = -3(7) + 24 = 3 (matches the table)

Since this function matches all values in the table, this is the correct model.

b. f(n) = -(1/3)n + 16:

Doesn't match the table values for all n.

c. f(n) = -3n + 64:

Doesn't match the table values for all n.

d. f(n) = -(1/3)n + 8:

Doesn't match the table values for all n.

Therefore, the function that models this situation is f(n) = -3n + 24. This model shows a linear relationship where the amount of pet food remaining decreases by 3 cups for every meal dispensed.