Question

question 12
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) = 40e^{-0.11t} ) units per liter of blood.
what is the concentration of the drug, in units per liter of blood, 5 hours after the injection? input your answer as a number (no labels) rounded accurate to two decimal places.

Explanation:

Step1: Identify the function and input

The concentration function is \( V(t) = 40e^{-0.11t} \), and we need to find \( V(5) \), so substitute \( t = 5 \) into the function.
\( V(5)=40e^{-0.11\times5} \)

Step2: Calculate the exponent

First, calculate the exponent part: \( -0.11\times5=-0.55 \)
So now we have \( V(5)=40e^{-0.55} \)

Step3: Evaluate the exponential term

We know that \( e^{-0.55}\approx e^{-0.55}\approx0.57695 \) (using a calculator for the exponential value)

Step4: Multiply by 40

Now multiply this value by 40: \( 40\times0.57695 = 23.078 \)

Step5: Round to two decimal places

Rounding \( 23.078 \) to two decimal places gives \( 23.08 \)

Answer:

23.08