Question

moving to another question will save this response.
question 1
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) = 45e^{-0.33t} ) 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.
moving to another question will save this response

Explanation:

Step1: Identify the function and input

We have the concentration function \( V(t) = 45e^{-0.35t} \) and we need to find \( V(5) \), so we substitute \( t = 5 \) into the function.
\( V(5)=45e^{-0.35\times5} \)

Step2: Calculate the exponent

First, calculate the exponent: \( - 0.35\times5=-1.75 \)
So now we have \( V(5) = 45e^{-1.75} \)

Step3: Evaluate the exponential term

We know that \( e^{-1.75}=\frac{1}{e^{1.75}} \). Calculate \( e^{1.75}\approx5.7546 \), so \( e^{-1.75}\approx\frac{1}{5.7546}\approx0.1738 \)

Step4: Multiply by 45

Now multiply this by 45: \( 45\times0.1738 = 7.821 \)

Step5: Round to two decimal places

Rounding \( 7.821 \) to two decimal places gives \( 7.82 \)

Answer:

7.82