At the end of a snow storm, Emily saw there was a lot of snow on her front lawn. The temperature increased and the snow began to melt at a steady rate. There was a depth of 15 inches of snow on the lawn when the storm ended and after 4 hours, the depth of snow was down to 12 inches. Write an equation for S,S, in terms of t,t, representing the depth of snow on Emily's lawn, in inches, tt hours after the snow stopped falling.

From the question, we are to write an equation for S, in terms of t, that represents the depth of the snow on Emily's lawn, t hours after the snow stopped falling

From the given information,

"There was a depth of 15 inches of snow on the lawn when the storm ended"

and

"after 4 hours, the depth of snow was down to 12 inches"

That is,

The snow has reduced by 15 - 12 inches after 4 hours

15 - 12 = 3

Thus,

The snow has reduced by 3 inches after 4 hours

Now,

If the snow reduced by 3 inches after 4 hours,

Then,

The snow will reduce by x inches after 1 hour

x = (3×1)/4

x = 3/4 inches

x = 0.75 inches

This means the snow reduces by 0.75 inches every hour.

Now,

After t hours, the snow would have reduced by 0.75t

Thus, the depth of the snow, S, after t hours will be

S = 15 - 0.75t

Hence, the equation that represents the depth of snow on Emily's lawn t hours after the snow stopped falling is

S = 15 - 0.75t

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