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To solve the problem step by step, we need to break down the information given in the question:

### Given:
1. \( C(f) = f^2 + f \), where \( 4 \leq f \leq 28 \), represents the average number of calories burned for walking \( f \) floors of stairs.
2. \( f(t) = t^2 + 3 \), where \( 1 \leq t \leq 5 \), represents the number of floors of stairs an average person can walk in \( t \) minutes.

### Question:
We are asked to determine the amount of calories a person will burn in **4 minutes** of walking the stairs.

### Step-by-step solution:

1. **Step 1**: Use \( t = 4 \) in the function \( f(t) \) to find the number of floors walked in 4 minutes.

   \[
   f(t) = t^2 + 3
   \]
   Substitute \( t = 4 \):
   \[
   f(4) = 4^2 + 3 = 16 + 3 = 19
   \]
   So, the person walks **19 floors** in 4 minutes.

2. **Step 2**: Now, we need to find how many calories are burned for walking these 19 floors. To do this, use the function \( C(f) = f^2 + f \), where \( f = 19 \).

   \[
   C(f) = f^2 + f
   \]
   Substitute \( f = 19 \):
   \[
   C(19) = 19^2 + 19 = 361 + 19 = 380
   \]

### Final Answer:
The person burns **380 calories** by walking for 4 minutes and covering 19 floors.

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Do you want further clarification on any of the steps or a more detailed explanation?

### Related questions:
1. How would the result change if the person walked for 3 minutes instead of 4?
2. What is the derivative of the function \( C(f) = f^2 + f \), and how does it relate to the rate of calorie burn?
3. If the number of floors walked follows a different pattern, like \( f(t) = 2t + 3 \), how would that impact the calorie calculation?
4. Can you determine how many minutes it would take to burn 500 calories?
5. What is the total calorie burn for walking 5 floors of stairs?

### Tip:
Always verify the units in applied problems to ensure you're calculating the right quantity, whether it's time, distance, or energy.

Determine the amount of calories a person will burn in 4 minutes of walking the stairs.

Determine the calories burned in 4 minutes of walking stairs by using quadratic functions. This problem involves function composition and is suitable for students in Grades 10-12.

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