Question

sports wanda is the manager for the soccer team. one of her duties is to hand out cups of water at practice. each cup of water is 4 ounces. she begins practice with a 128-ounce cooler of water.
a. create a function to represent the arithmetic sequence.
a) $f(n) = 128 + (n - 1)(4)$
b) $f(n) = 128 + (n - 1)(-4)$
c) $f(n) = -128 + (n - 1)(4)$
d) $f(n) = -128 + (n - 1)(-4)$
part b
b. how much water is remaining after wanda hands out the 14th cup?
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Explanation:

Part a

Step1: Recall Arithmetic Sequence Formula

The formula for the \(n\)-th term of an arithmetic sequence is \(f(n)=f(1)+(n - 1)d\), where \(f(1)\) is the first term and \(d\) is the common difference.
Here, the initial amount of water (first term \(f(1)\)) is 128 ounces. Since we are handing out cups of water, the amount of water is decreasing, so the common difference \(d=- 4\) (because each cup is 4 ounces, so we subtract 4 per cup).

Step2: Identify the Correct Function

Substituting \(f(1) = 128\) and \(d=-4\) into the formula \(f(n)=f(1)+(n - 1)d\), we get \(f(n)=128+(n - 1)(-4)\), which is option B.

Step1: Use the Function from Part a

We have the function \(f(n)=128+(n - 1)(-4)\). We need to find the amount of water remaining after \(n = 14\) cups are handed out.

Step2: Substitute \(n = 14\) into the Function

Substitute \(n = 14\) into \(f(n)\):

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Answer:

B) \(f(n)=128+(n - 1)(-4)\)

Part b