Question

At the end of a snow storm, Tristan saw there was a lot of snow on his front lawn. The
temperature increased and the snow began to melt at a steady rate. After the storm,
the snow started melting at a rate of 0.75 inches per hour and it is known that 4 hours
after the storm ended, the depth of snow was down to 9 inches. Write an equation for
S, in terms of t, representing the depth of snow on Tristan's lawn, in inches, t hours
after the snow stopped falling.

Answer 1

Answer:$S(t)=12-0.75t$

Step-by-step explanation:

Given: The snow started melting at a rate of 0.75 inches per hour and it is known that 4 hours  after the storm ended, after the storm ended, the depth of snow was down to 9 inches.

Snow melted in 4 hours = $0.75\times4 =3\text{ inches}$

Initial depth of snow = 9 + 3 inches = 12 inches.

Now, depth of snow on Tristan's lawn = Initial depth -0.75(Number of hours)

Let S(t) be the depth of snow on Tristan's lawn, in inches, t hours after the snow stopped falling.

Then, $S(t)=12-0.75t$

Answer 2

The linear equation that represents the depth of snow on Tristan's lawn, in inches, t hours  after the snow stopped falling is:

$S(t) = 12 - 0.75t$

A linear function in the model will have the following format:

$S(t) = S(0) - mt$

In which:

• S(0) is the initial amount of snow.
• m is the melting rate, which is the slope.

The snow melts at a rate of 0.75 inches per hour, thus $m = 0.75$ and:

$S(t) = S(0) - 0.75t$

After 4 hours, there were 9 inches, that is, when $t = 4, S(t) = 9$, and this is used to find S(0).

$S(t) = S(0) - 0.75t$

$9 = S(0) - 0.75(4)$

$S(0) = 9 + 0.75(4)$

$S(0) = 12$

Hence, the equation is:

$S(t) = 12 - 0.75t$

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