Question

question 2 of 14, step 1 of 1 the concentration c(t) of a certain drug in the bloodstream after t minutes is given by the formula c(t) = 0.09(1 - e^{-0.2t}). what is the concentration after 12 minutes? round to three decimal places.

Explanation:

Step1: Substitute \( t = 12 \) into the formula

Given \( C(t)=0.09(1 - e^{-0.2t}) \), when \( t = 12 \), we have \( C(12)=0.09(1 - e^{-0.2\times12}) \).
First, calculate the exponent: \( - 0.2\times12=-2.4 \).

Step2: Calculate \( e^{-2.4} \)

We know that \( e^{-x}=\frac{1}{e^{x}} \), so \( e^{-2.4}\approx0.090717953 \).

Step3: Calculate \( 1 - e^{-2.4} \)

\( 1 - e^{-2.4}=1 - 0.090717953 = 0.909282047 \).

Step4: Calculate \( C(12) \)

\( C(12)=0.09\times0.909282047\approx0.082 \).

Answer:

\( 0.082 \)