To solve this question, we need to analyze the given function related to the depth of snow over time and identify the correct descriptive statement.
### Given Information:
- The function is [tex]\( f(n+1) = f(n) + 0.8 \)[/tex].
- The initial depth of snow is [tex]\( f(0) = 2.5 \)[/tex] inches.
### Analyzing the Function:
1. Initial Depth:
- The initial depth of the snow when the storm began is given by [tex]\( f(0) = 2.5 \)[/tex] inches. This is the starting value of the sequence.
2. Rate of Increase:
- According to the function [tex]\( f(n+1) = f(n) + 0.8 \)[/tex], the snow increases by 0.8 inches every hour.
### Choosing the Correct Statement:
- Let's evaluate the provided options one by one based on the initial depth and the rate of increase.
1. Option 1:
- "The depth of snow was 0.8 inches when the storm began, and 2.5 inches after the first hour of the storm."
- Incorrect: The initial depth is actually 2.5 inches, not 0.8 inches.
2. Option 2:
- "The depth of snow was 1.7 inches when the storm began, and 0.8 inches of snow fell each hour."
- Incorrect: The initial depth is actually 2.5 inches, not 1.7 inches.
3. Option 3:
- "The depth of snow was 2.5 inches when the storm began, and increased by 0.8 inches each hour."
- Correct: This matches exactly with our calculation where the initial depth is 2.5 inches and the snow increases by 0.8 inches each hour.
4. Option 4:
- "The depth of snow was 3.3 inches when the storm began, and 2.5 inches of snow fell in 1 hour."
- Incorrect: The initial depth is 2.5 inches, and the rate of increase is 0.8 inches every hour, not 2.5 inches.
### Conclusion:
The correct statement that describes the sequence of numbers generated by the function is:
"The depth of snow was 2.5 inches when the storm began, and increased by 0.8 inches each hour."
