Answer:
The piecewise equation is given as :
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
The rain then slows down and remains constant
So, Amount of rain for that hour =
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 =
The rain increases at a rate of 20t from 4 ≤ x ≤ 6.
Hence the piecewise equation is given as :