Question

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

Answer 1

Answer:

The piecewise equation is given as :$A(t)=\begin{cases} 25x& \text{ if } 0 \leq x \leq 3 \\ 75& \text{ if } 3$

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

$A(x) = 25x ; 0 \leq x \leq 3$

The rain then slows down and remains constant

So, Amount of rain for that hour = $25 \times 3 = 75 mm$

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 = $75+20(x-4) ; 4 \leq x\leq 6$

The rain increases at a rate of 20t from 4 ≤ x ≤ 6.

Hence the piecewise equation is given as :$A(t)=\begin{cases} 25x& \text{ if } 0 \leq x \leq 3 \\ 75& \text{ if } 3$