Question

question 7 it is estimated that t hours after an injection of an experimental drug, the concentration of that drug in the bloodstream is given by $v(t) = 49e^{-0.1t}$ 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: Substitute \( t = 5 \) into the function \( V(t) \)

We have the function \( V(t)=49e^{-0.11t} \). When \( t = 5 \), we substitute \( t \) with 5 in the function, so we get \( V(5)=49e^{-0.11\times5} \).

Step2: Calculate the exponent

First, calculate the value of the exponent: \( - 0.11\times5=-0.55 \). So now the function becomes \( V(5) = 49e^{-0.55} \).

Step3: Calculate the value of \( e^{-0.55} \)

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

Step4: Multiply by 49

Now, multiply 49 by the value of \( e^{-0.55} \): \( 49\times0.57695 = 28.27055 \).

Step5: Round to two decimal places

Rounding 28.27055 to two decimal places, we look at the third decimal digit which is 0. Since \( 0<5 \), we round down. So we get 28.27.

Answer:

28.27