Question

There was no snow on the ground when it started falling at midnight at a constant rate of 1.5 inches per hour. At

Answer 1

Answer:

The depth of snow at 9:00 am was 19 inches.

Step-by-step explanation:

Consider the provided information.

Let x represents the number of hours and S(x) represents the depth of snow.

There was no snow on the ground when it started falling at midnight at a constant rate of 1.5 inches per.

That means the depth of snow will be:

$S(x)=1.5x\ \ \ 0\leq x< 4$

At  4:00 a.m., it starting falling at a constant rate of 3 inches per hour,

$S(x)=3(x-4)+6\ \ \ 4\leq x$

7:00 a.m. to 9:00 a.m., snow was  falling at a constant rate of 2 inches per hour.

$S(x)=2(x-7)+15\ \ \ 7\leq x\leq 9$

The required piece-wise linear function is

$\left\{\begin{matrix}1.5x & 0\leq x$

We need to find the how deep was the snow at 9:00 am

For 9:00 am we will choose the function which can take the value of x=9

Substitute the value of x=9 in $S(x)=2(x-7)+15$

$S(x)=2(9-7)+15$

$S(x)=2(2)+15$

$S(x)=19$

Hence, the depth of snow at 9:00 am was 19 inches.