Questions: It is estimated that t hours after an injection of an experimental drug, the concentration of that drug in the bloodstream is given by V(t)=65 e^(-0.36 t) units per liter of blood. What is the concentration of the drug, in units per liter of blood, 3 hours after the injection? Input your answer as a number (no labels) rounded accurate to two decimal places. 22.07

Solution Steps

To find the concentration of the drug 3 hours after the injection, we need to evaluate the function \( V(t) = 65 e^{-0.36 t} \) at \( t = 3 \). This involves substituting \( t = 3 \) into the function and calculating the result.

The concentration of the drug in the bloodstream is given by the function: \[ V(t) = 65 e^{-0.36 t} \]

To find the concentration 3 hours after the injection, substitute \( t = 3 \) into the function: \[ V(3) = 65 e^{-0.36 \cdot 3} \]

Calculate the value of the exponential term: \[ e^{-0.36 \cdot 3} = e^{-1.08} \approx 0.3396 \]

Multiply the result by 65: \[ V(3) = 65 \cdot 0.3396 \approx 22.0737 \]

Round the result to two decimal places: \[ V(3) \approx 22.07 \]

Final Answer