Given:
Nana has a water purifier that filters
of the contaminants each hour.
Water has contaminants =

To find:
The function that gives the remaining amount of contaminants in kilograms, C(t), t hours after Nana started purifying the water.
Solution:
Let C(t) be the remaining amount of contaminants in kilograms after t hours.
Initial amount of contaminants =

Decreasing rate is
.
Using the exponential decay model:

where,
is initial amount of contaminants, r is the decreasing rate and t is time in hours.
Substituting the values, we get


Therefore, the required function is
.