Given:
Nana has a water purifier that filters [tex]\dfrac{1}{3}[/tex] of the contaminants each hour.
Water has contaminants = [tex]\dfrac{1}{2}[/tex]
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 = [tex]\dfrac{1}{2}[/tex]
Decreasing rate is [tex]\dfrac{1}{3}[/tex] .
Using the exponential decay model:
[tex]C(t)=C_0(1-r)^t[/tex]
where, [tex]C_0[/tex] is initial amount of contaminants, r is the decreasing rate and t is time in hours.
Substituting the values, we get
[tex]C(t)=\dfrac{1}{2}(1-\dfrac{1}{3})^t[/tex]
[tex]C(t)=\dfrac{1}{2}(\dfrac{2}{3})^t[/tex]
Therefore, the required function is [tex]C(t)=\dfrac{1}{2}(\dfrac{2}{3})^t[/tex].
Answer:
[tex]\frac{1}{2} (\frac{2}{3} )^t[/tex]
Step-by-step explanation:
It's correct on Khan.
