Question

2. During typhoon Ambo, PAGASA tracks the amount of accumulating rainfall. For

the first three hours of typhoon, the rain fell at a constant rate of 25mm per
hour.
The typhoon slows down for an hour and started again at a constant rate of 20 mm
per hour for the next two hours. Write a piecewise function that models the amount
of rainfall as function of time.​

Answer 1

The answer is below

Explanation:

Let t represent the time in hour and A(t) represent the amount of accumulating rainfall at time t.

In the first three hours the rain fell at a constant rate of 25mm per

hour, hence:

A(t) = 25t 0 ≤ t ≤ 3

The rain then slows down and remains constant at 75 mm [i.e. 25(3)] for an hour.

The rain increases at a rate of 20t from 4 ≤ t ≤ 6. Hence the piecewise equation is given as:

`A(t)=\left \{ {{25t\ \ \ \ \ \ \ \ \ \ for\ 0\leq\ t\ \leq\ 3} \atop {75\ \ \ \ \ \ \ \ \ \ for\ 0\leq\ t\ \leq\ 6 \atop {75+20(t-4)\ \ for\ 4\ \leq\ t\ \leq\ 6}} } \right. \\\\\left`