`f(s)=(s)/(25)+1`
A collage compus has vending machines which must be peroidically restocked. The restocking frequency depends primarily on how many students have class near the machine each semester. The vending machine company uses the function shown above, where s is the number of students estimated too have classes within the immediate vicinity on a daily basis, to determine how many times per semester the machine must be restocked. How many more times must a vending machine that has 400 students in the immediate vicinity be restocked compared to one that has 300 students in the immediate vicinity?

Options

A. `2`
B. `4`
C. `7`
D. `13`

Explanation

To solve the problem, we need to find the number of times the vending machine must be restocked for two different scenarios: when there are 400 students and when there are 300 students. We will use the function given, \( f(s) = \frac{s}{25} + 1 \).

### Step 1: Calculate the restocking frequency for 400 students
We will substitute \( s = 400 \) into the function.

\[ f(400) = \frac{400}{25} + 1 \]

### Step 2: Simplify the calculation
First, calculate \( \frac{400}{25} \):

\[ \frac{400}{25} = 16 \]

Now, add 1:

\[ f(400) = 16 + 1 = 17 \]

So, the vending machine must be restocked 17 times for 400 students.

### Step 3: Calculate the restocking frequency for 300 students
Now, we will substitute \( s = 300 \) into the function.

\[ f(300) = \frac{300}{25} + 1 \]

### Step 4: Simplify the calculation
First, calculate \( \frac{300}{25} \):

\[ \frac{300}{25} = 12 \]

Now, add 1:

\[ f(300) = 12 + 1 = 13 \]

So, the vending machine must be restocked 13 times for 300 students.

### Step 5: Find the difference in restocking frequency
Now, we need to find out how many more times the machine must be restocked for 400 students compared to 300 students.

\[ \text{Difference} = f(400) - f(300) = 17 - 13 = 4 \]

Thus, the vending machine that has 400 students in the immediate vicinity must be restocked 4 more times compared to one that has 300 students.

### Final Answer
The vending machine must be restocked **4 more times** for 400 students compared to 300 students.

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