The concentration $C(t)$ of a certain drug in the bloodstream after $t$ minutes is given by the formula $C(t)=0.04\left(1-e^{-0.2 t}\right)$. What is the concentration 6 fter 5 minutes? Round to three decimal places.
Answer
Final Answer: The concentration of the drug in the bloodstream after 5 minutes is approximately \(\boxed{0.025}\).
Step 1 ：The concentration $C(t)$ of a certain drug in the bloodstream after $t$ minutes is given by the formula $C(t)=0.04\left(1-e^{-0.2 t}\right)$.
Step 2 ：We are asked to find the concentration of the drug in the bloodstream after 5 minutes. This can be calculated by substituting $t=5$ into the given formula.
Step 3 ：Substituting $t=5$ into the formula, we get $C(5)=0.04\left(1-e^{-0.2 \times 5}\right)$.
Step 4 ：Solving the equation, we get $C(5) = 0.025284822353142306$.
Step 5 ：Rounding to three decimal places, we get $C(5) = 0.025$.
Step 6 ：Final Answer: The concentration of the drug in the bloodstream after 5 minutes is approximately \(\boxed{0.025}\).
