Answer:
The piecewise equation is given as :[tex]A(t)=\begin{cases} 25x& \text{ if } 0 \leq x \leq 3 \\ 75& \text{ if } 3<x<4 \\ 75+20(x-4) & \text{ if } 4 \leq x \leq 6\end{cases}[/tex]
Step-by-step explanation:
Let x be the time in hour and A(x) be the amount of accumulating rainfall at time x.
We are given that in the first three hours the rain fell at a constant rate of 25mm per hour
Amount of rainfall in 1 hour = 25
Amount of rainfall in t hours = 25x
[tex]A(x) = 25x ; 0 \leq x \leq 3[/tex]
The rain then slows down and remains constant
So, Amount of rain for that hour = [tex]25 \times 3 = 75 mm[/tex]
75 mm ; 3
Now we are given that started again at a constant rate of 20 mm per hour for the next two hours.
Amount of rain after 4 hours = [tex]75+20(x-4) ; 4 \leq x\leq 6[/tex]
The rain increases at a rate of 20t from 4 ≤ x ≤ 6.
Hence the piecewise equation is given as :[tex]A(t)=\begin{cases} 25x& \text{ if } 0 \leq x \leq 3 \\ 75& \text{ if } 3<x<4 \\ 75+20(x-4) & \text{ if } 4 \leq x \leq 6\end{cases}[/tex]
