At the end of a snow storm, Mason 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 10 inches of snow on the lawn when the storm ended and then it started melting at a rate of 0.5 inches per hour. Write an equation for the function S (t), representing the depth of snow on Mason's lawn, in inches, t hours after the snow stopped falling.

S (t) = 10 - 0.5t

Step-by-step explanation:

initial depth of snow = 10 inches

melting rate = 0.5 inches per hour

it means that, in one hour snow depth will decrease by 0.5 inches

thus, in t hours snow depth will decrease by 0.5*t = 0.5t inches

Thus, depth of snow after t hours can be calculated by

we will take initial depth of snow and them subtract the depth of snow which melted in t hours.

we are subtracting as snow is melting and will thus decrease the depth of snow

depth of snow after t hours can = initial depth of snow - decrease of the depth of snow after snow melts for t hours

depth of snow after t hours can = 10 inches - 0.5t inches

= (10 - 0.5t) inches

Thus, S (t), representing the depth of snow on Mason's lawn, in inches, t hours after the snow stopped falling is S (t) = 10 - 0.5t