To determine the concentration [tex]\( C(t) \)[/tex] of the drug in the bloodstream after [tex]\( t = 11 \)[/tex] minutes, we use the given formula:
[tex]\[ C(t) = 0.04 \left(1 - e^{-0.2 t}\right) \][/tex]
Let's break down the steps to find [tex]\( C(11) \)[/tex]:
1. Substitute [tex]\( t = 11 \)[/tex] into the formula:
[tex]\[ C(11) = 0.04 \left(1 - e^{-0.2 \cdot 11}\right) \][/tex]
2. Calculate the exponent:
[tex]\[ -0.2 \cdot 11 = -2.2 \][/tex]
3. Evaluate the exponential part:
[tex]\[ e^{-2.2} \][/tex]
Here, we find the value of the exponential function at [tex]\(-2.2\)[/tex].
4. Subtract the exponential result from 1:
[tex]\[ 1 - e^{-2.2} \][/tex]
5. Multiply the result by 0.04:
[tex]\[ C(11) = 0.04 \left(1 - e^{-2.2}\right) \][/tex]
After performing these calculations, the concentration [tex]\( C(11) \)[/tex] is found to be approximately [tex]\( 0.036 \)[/tex]. When rounded to three decimal places, the concentration of the drug in the bloodstream after 11 minutes is:
[tex]\[ \boxed{0.036} \][/tex]
