Questions: Determine the concentration of the drug at a specific time t: The concentration C(t) (in milligrams per liter, mg / L ) of a drug in the blood stream t hours after the drug is administered is modeled by C(t) = 14 t / (6 t^2 + 5)

Solution Steps

To determine the concentration of the drug at a specific time \( t \), we need to evaluate the function \( C(t) = \frac{14t}{6t^2 + 5} \) at the given time \( t \). This involves substituting the value of \( t \) into the function and computing the result.

The concentration \( C(t) \) of the drug in the bloodstream at time \( t \) hours is given by the formula: \[ C(t) = \frac{14t}{6t^2 + 5} \]

To find the concentration at \( t = 2 \), we substitute \( t \) into the function: \[ C(2) = \frac{14 \cdot 2}{6 \cdot 2^2 + 5} \]

Calculating the numerator and denominator:

• Numerator: \( 14 \cdot 2 = 28 \)
• Denominator: \( 6 \cdot 2^2 + 5 = 6 \cdot 4 + 5 = 24 + 5 = 29 \)

Thus, we have: \[ C(2) = \frac{28}{29} \approx 0.9655 \]

Final Answer