Question

Read and analyze each situation carefully and apply your learnings on representing
real-life situations involving functions including piecewise.
1. Contaminated water is subjected to a cleaning process. The concentration of the
pollutants is initially 5 mg per liter of water. If the cleaning process can reduce the
pollutant by 10% each hour, define a function that can represent the concentration
of pollutants in the water in terms of the number of hours that the cleaning process
has taken place.
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

Answer:

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Step-by-step explanation:

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Answer 2

Given - Contaminated water is subjected to a cleaning process. The concentration of the pollutants is initially 5 mg per liter of water. Pollutants are reduced by 10% by each hour by cleaning process.

Find out-  Concentration of pollutants in the water in terms of the number of hours that cleaning process has taken place.

Solution and explanation -

Pollutants are 5 mg per liter

After one hour = 5(1-10/100) = 0.9×5

After two hours = 0.9×5 (1-10/100) = 0.9²× 5

After three hours = 0.9²× 5 (1-10/100) = 0.9³× 5

After n hours = 0.9ⁿₓ5  

Answer : f(n) = 0.9ⁿₓ5 mg/litre

n = Number of hours.

f(n) = Function that represents the concentration.

Given -PAGASA tracks the amount of rainfall for typhoon Ambo and for the first 3 hours rain fell at a constant rate of 25 mm per hour. Then typhoon slows down and rain fell at a constant rate of 20mm per hour for 2 hours.

We have to do - Write a piecewise function that models the amount of rainfall as function of time.

Solution and explanation - For the first 3 hours rain fell at a constant rate of 25 mm per hour.

R(t) = 25 for 0<t ≤3

Then the next hour no typhoon happend

Rain in 3 hours = 75

R(t) = 75 for 3 <t≤4

Started again for next 2 hours  at a rate of 20mm per hour.

R(t) = 75+20 (t-4)

for 4<t≤6

R(t) = 20t -5 for 4<t≤6

Answer :  Function piece wisely R (t) in mm is

25t 0<t≤3

75 3<t≤4

20t-5  4<t≤6

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