Question

Nana has a water purifier that filters \dfrac13 3 1 ​ start fraction, 1, divided by, 3, end of the contaminants each hour. She used it to purify water that had \dfrac12 2 1 ​ start fraction, 1, divided by, 2, end fraction kilogram of contaminants. Write a function that gives the remaining amount of contaminants in kilograms, C(t)C(t)C, left parenthesis, t, right parenthesis, ttt hours after Nana started purifying the water.

Answer 1

(1/2) * (2/3)^t

Explanation:

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)=

The water purifier will filter 1/3 of the current contaminants each hour.

1/3 ÷ 1/2

= 1/3 × 2/1

= 2/3

This means, it willreduce the contaminant into 2/3 of it current mass

To derive the equation,

Multiply the contaminant with 2/3 every hour

(1/2) * (2/3)^t

Where t = hours