The domain of the function is 0 ≤ t ≤ 3 and the greatest concentration of the medication is 2mg/L
<h3>The domain of the function</h3>The equation of the function is given as:
Time can be 0 or greater but cannot be negative.
So, the domain of the function includes t ≥ 0
Set the function to 0 to determine the maximum value of t.
Cross multiply
Factor out -18t
-18t(t - 3) = 0
Divide both sides by -18t
t - 3 = 0
Add 3 to both sides
t = 3
This means that the maximum value of t is 3
Hence, the domain of the function is 0 ≤ t ≤ 3
<h3>The greatest concentration of the medication</h3>From the graph of the function (see attachment), we have the maximum value to be;
C(t) = 2
Hence, the greatest concentration of the medication is 2mg/L
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