The depth of snow after n hours of a snowstorm is represented by the function f(n + 1) = f(n) + 0.8 where f(0) = 2.5. Which statement describes the sequence of numbers generated by the function?

To analyze the given function \( f(n + 1) = f(n) + 0.8 \) with the initial condition \( f(0) = 2.5 \), we can calculate the depth of snow for subsequent hours.

• At \( n = 0 \): \( f(0) = 2.5 \) inches.

• At \( n = 1 \): \( f(1) = f(0) + 0.8 = 2.5 + 0.8 = 3.3 \) inches.

• At \( n = 2 \): \( f(2) = f(1) + 0.8 = 3.3 + 0.8 = 4.1 \) inches.

This shows that the function represents a sequence where the depth of snow starts at 2.5 inches when the storm began (at \( n = 0 \)) and increases by 0.8 inches with each passing hour.

Now let's analyze the statements:

1. "The depth of snow was 0.8 inches when the storm began, and 2.5 inches after the first hour of the storm."

   • This is incorrect because the initial depth was 2.5 inches, not 0.8 inches.

2. "The depth of snow was 1.7 inches when the storm began, and 0.8 inches of snow fell each hour."

   • This is also incorrect as the initial depth was 2.5 inches, not 1.7 inches.

3. "The depth of snow was 2.5 inches when the storm began, and increased by 0.8 inches each hour."

   • This statement is correct as it accurately reflects the initial depth and the rate of increase.

4. "The depth of snow was 3.3 inches when the storm began, and 2.5 inches of snow fell in 1 hour."

   • This is incorrect as the depth when the storm began was 2.5 inches, not 3.3 inches.

Thus, 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."