Question

during a snowstorm the snow fell 57.75 inches deep. due to rising temperatures, the snow is melting at a rate of 6.25 inches per day. consider function g where g(x) represent the amount of snow, in inches, that is left after x days. a. create the function g(x) b. evaluate g(0) and explain what the solution means within the context of the problem. c. evaluate g(5) and explain what the solution means within the context of the problem.

Explanation:

Step1: Create the function

The initial amount of snow is \(57.75\) inches and it melts at a rate of \(6.25\) inches per day. Using the linear function formula \(y = mx + b\) (where \(m\) is the slope and \(b\) is the y - intercept), here \(m=-6.25\) (negative because it's melting) and \(b = 57.75\). So \(g(x)=-6.25x + 57.75\).

Step2: Evaluate \(g(0)\)

Substitute \(x = 0\) into \(g(x)\): \(g(0)=-6.25\times0+57.75 = 57.75\). This means that at day \(0\) (the start of the melting process), there is \(57.75\) inches of snow.

Step3: Evaluate \(g(5)\)

Substitute \(x = 5\) into \(g(x)\): \(g(5)=-6.25\times5+57.75=-31.25 + 57.75=26.5\). This means that after \(5\) days of melting, there is \(26.5\) inches of snow left.

Answer:

A. \(g(x)=-6.25x + 57.75\)
B. \(g(0) = 57.75\), it means the initial amount of snow (at day \(0\)) is \(57.75\) inches.
C. \(g(5)=26.5\), it means after \(5\) days of melting, there is \(26.5\) inches of snow left.