A linear function can be used to estimate the decrease in snowfall measured since 1920. The decrease in the annual snowfall has been on average 0.24 inches per year. Let x represent the number of years since 1920, when the measurements began, and let y represent the annual snowfall. The initial measurement in 1920 was 48.6 inches. Using the average change and initial measurement, which is the best estimate of the annual snowfall in the 78th year after records were kept? Round to the nearest hundredth.

Question

15.84 inches
27.72 inches
29.88 inches
67.32 inches

Answer 1

To determine the estimate of the annual snowfall in the 78th year after records began (which is the year 1998), we can use the linear function based on the given information.

1. Identify the variables:

   • Initial measurement \( y_0 = 48.6 \) inches (in 1920, or when \( x = 0 \))
   • Average decrease in snowfall per year = \( -0.24 \) inches/year
   • We want to find \( y \) when \( x = 78 \) (the year 1998).

2. Define the linear function: \[ y = y_0 + \text{(slope)} \cdot x \]

3. Plug in the values:

   • The slope (rate of change) is \( -0.24 \).
   • \( y_0 = 48.6 \).
   • Substitute \( x = 78 \).

   \[ y = 48.6 - 0.24 \cdot 78 \]

4. Calculate: \[ 0.24 \cdot 78 = 18.72 \] \[ y = 48.6 - 18.72 = 29.88 \]

5. Round to the nearest hundredth: The result is \( 29.88 \) inches.

Thus, the best estimate of the annual snowfall in the 78th year after records began is 29.88 inches.