Question

question 2 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) = 120e^{-0.12t} units per liter of blood. what is the concentration of the drug, in units per liter of blood, 20 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 \( V(t) = 120e^{-0.12t} \) and we need to find \( V(20) \), so we substitute \( t = 20 \) into the function.
\( V(20)=120e^{-0.12\times20} \)

Step2: Calculate the exponent

First, calculate the value of the exponent: \( - 0.12\times20=-2.4 \)
So now the function becomes \( V(20) = 120e^{-2.4} \)

Step3: Evaluate the exponential term

We know that \( e^{-2.4}=\frac{1}{e^{2.4}} \). Using a calculator, \( e^{2.4}\approx11.02317638 \), so \( e^{-2.4}\approx\frac{1}{11.02317638}\approx0.09071795 \)

Step4: Multiply by 120

Now multiply this value by 120: \( 120\times0.09071795 = 10.886154 \)

Step5: Round to two decimal places

Rounding \( 10.886154 \) to two decimal places gives \( 10.89 \) (since the third decimal place is 6, which is greater than 5, we round up the second decimal place).

Answer:

10.89