Nana has a water purifier that filters 1/3 of the contaminants each hour. she used it to purify water that had 1/2 kilogram of contaminants.

write a function that gives the remaining amount of contaminants in kilograms, c(t), t hours after nana started purifying the water.

c(t)=

C(t)= 0.5kg* (2/3) ^ t

Step-by-step explanation:

The water purifier will filter 1/3 of the current contaminants each hour. In other words, it will reduce the contaminant into 2/3 of it current mass. If the contaminant 1 kg, after 1 hour will be 2/3 kg, then become 4/9 kg after 2 hours. You have to multiply the contaminant with 2/3 every hour.

The equation will be

C(t)= X * (2/3) ^ t  

C(t)= 0.5* (2/3) ^ t

Step-by-step explanation:

We know that the water purifier filters 1/3 kg of contaminant per hour, that can be expressed as

Where is time in hours.

Then, the problem states that Nana needs to purify water that has 1/2 kg of contaminants. In other words, the initial condition of the function is 1/2.

Uniting all these, we can express the situation as

Where is the contaminant remaining in kilograms.

The function has to have a subtraction, because the purifier does that, it subtract contaminant from the water.

Therefore, the function that modelates this situation is

what is the starting amount? the question is not clear sorry.

step-by-step explanation:

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explanation: