Respuesta :
Answer:
The required piece-wise linear function is
[tex]\left\{\begin{matrix}1.5x & 0\leq x<4\\ 3(x-4)+6 & 4\leq x<7\\ 2(x-7)+15 & 7\leq x\leq 9\end{matrix}\right.[/tex]
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:
[tex]S(x)=1.5x\ \ \ 0\leq x< 4[/tex]
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,
[tex]S(x)=3(x-4)+6\ \ \ 4\leq x<7 [/tex]
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
[tex]S(x)=2(x-7)+15\ \ \ 7\leq x\leq 9 [/tex]
Therefore, the required piece-wise linear function is
[tex]\left\{\begin{matrix}1.5x & 0\leq x<4\\ 3(x-4)+6 & 4\leq x<7\\ 2(x-7)+15 & 7\leq x\leq 9\end{matrix}\right.[/tex]
