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 required piece-wise linear function is

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

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,

From mid night to 4:00 a.m the depth of snow will be 1.5×4=6 inches.

If we want to calculate the total depth of snow from midnight to 7:00 am we need to add 6 inches in 3(x-4) where 4≤x<7

Therefore,

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

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

From mid night to 7:00 a.m the depth of snow will be 3(7-4)+6=15 inches.

If we want to calculate the total depth of snow from midnight to 9:00 am we need to add 15 inches in 2(x-7) where 7≤x≤9

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

Therefore, the required piece-wise linear function is

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