Question: Question 7 of 12, Step 1 of 1 The concentration \( C(t) \) of a certain drug in the bloodstream…

Question 7 of 12, Step 1 of 1

The concentration \( C(t) \) of a certain drug in the bloodstream after \( t \) minutes is given by the formula \( C(t) = 0.07(1 - e^{-0.2t}) \). What is the concentration after 11 minutes? Round to three decimal places.

Answer

How to enter your answer (opens in new window)

drug concentration =

Solution

The concentration \( C(t) \) of a certain drug in the bloodstream after \( t \) minutes is given by the formula: \[ C(t) = 0.07 \left( 1 - e^{-0.2t} \right) \] We need to find the concentration after 11 minutes. Substitute \( t = 11 \) into the formula: \[ C(11) = 0.07 \left( 1 - e^{-0.2 \times 11} \right) \] Calculate the exponent: \[ -0.2 \times 11 = -2.2 \] Compute the exponential function: \[ e^{-2.2} \approx 0.1108 \] Substitute back into the formula: \[ C(11) = 0.07 \left( 1 - 0.1108 \right) \] Simplify: \[ C(11) = 0.07 \times 0.8892 \] Calculate the final answer: \[ C(11) \approx 0.062244 \] Round to three decimal places: \[ C(11) \approx 0.062 \] So, the concentration after 11 minutes is approximately 0.062.