Question

At the end of a snow storm, Hudson saw there was a lot of snow on his front lawn. The temperature increased and the snow began to melt at a steady rate. There was a depth of 18 inches of snow on the lawn when the storm ended and then it started melting at a rate of 2 inches per hour. Make a table of values and then write an equation for S, commaS, in terms of t, commat, representing the depth of snow on Hudson's lawn, in inches, tt hours after the snow stopped falling.

Answer 1

To create a table of values and write an equation representing the depth of snow on Hudson's lawn in inches over time, we can start with the initial conditions provided. Initially, the depth of the snow is 18 inches and it melts at a steady rate of 2 inches per hour.

Table of Values

We will calculate the depth of snow for various values of \( t \) (time in hours) until the snow has completely melted.

| \( t \) (hours) | Depth of Snow \( S \) (inches) | |------------------|------------------------| | 0 | 18 | | 1 | 18 - 2(1) = 16 | | 2 | 18 - 2(2) = 14 | | 3 | 18 - 2(3) = 12 | | 4 | 18 - 2(4) = 10 | | 5 | 18 - 2(5) = 8 | | 6 | 18 - 2(6) = 6 | | 7 | 18 - 2(7) = 4 | | 8 | 18 - 2(8) = 2 | | 9 | 18 - 2(9) = 0 |

Equation

The equation for the depth of snow \( S \) in inches, in terms of \( t \) (hours after the snow stopped falling), can be expressed as:

\[ S(t) = 18 - 2t \]

This equation shows that starting with 18 inches of snow, the depth decreases by 2 inches for each hour \( t \).

Important Note

The snow will completely melt when \( S(t) \) reaches 0 inches. To find when this occurs:

\[ 0 = 18 - 2t \implies 2t = 18 \implies t = 9 \]

Thus, the snow completely melts after 9 hours.