Question

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?

• the depth of snow was 0.8 inches when the storm began, and 2.5 inches after the first hour of the storm.
• the depth of snow was 1.7 inches when the storm began, and 0.8 inches of snow fell each hour.
• the depth of snow was 2.5 inches when the storm began, and increased by 0.8 inches each hour.
• the depth of snow was 3.3 inches when the storm began, and 2.5 inches of snow fell in 1 hour.

Explanation:

Identify the initial value of the function

$$ f(0) = 2.5 $$

Analyze the recursive rate of change

$$ f(n + 1) = f(n) + 0.8 $$

Interpret the parameters in context

$$
LATEXBLOCK0
$$

Answer:

• The depth of snow was 0.8 inches when the storm began, and 2.5 inches after the first hour of the storm.
• The depth of snow was 1.7 inches when the storm began, and 0.8 inches of snow fell each hour.
• The depth of snow was 2.5 inches when the storm began, and increased by 0.8 inches each hour. (Correct answer)
• The depth of snow was 3.3 inches when the storm began, and 2.5 inches of snow fell in 1 hour.