Question

question 8
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) = 95e^{-0.15t} ) units per liter of blood.
what is the concentration of the drug, in units per liter of blood, 15 hours after the injection? input your answer as a number (no labels) rounded accurate to two decimal places.

Explanation:

Step1: Substitute t = 15 into the function

We have the function \( V(t) = 95e^{-0.1t} \). Substitute \( t = 15 \) into it: \( V(15)=95e^{-0.1\times15} \)

Step2: Calculate the exponent

First, calculate the exponent: \( -0.1\times15=-1.5 \)

Step3: Calculate the exponential term

Now, calculate \( e^{-1.5} \). We know that \( e^{-1.5}\approx0.2231301601 \)

Step4: Multiply by 95

Multiply this value by 95: \( 95\times0.2231301601 = 21.19736521 \)

Step5: Round to two decimal places

Rounding 21.19736521 to two decimal places gives 21.20

Answer:

21.20