Question

Nana has a water purifier that filters

\[\dfrac{1}3\] of the contaminants each hour. She used it to purify water that had

\[\dfrac{1}2\] 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.

Answer 1

Each hour the purifier leaves 1 − 1/3 = 2/3 of the contaminants. Starting with 1/2 kg, after t hours the amount is
C(t) = (1/2) (2/3)^t kilograms,
for t ≥ 0 (t an integer if you count whole hours; equivalently C(t) = (1/2)e^{t ln(2/3)} for real t).