Question

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)=

Answer 1

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

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