Rate of Change in Drug Concentration Over Time

What is the rate of change in drug concentration after 1.3 hours?

Given the function C(t) = 2.1te^-1.3t, how fast is the concentration changing in 1.3 hours?

Rate of Change in Drug Concentration

The rate at which the concentration of the drug is changing in 1.3 hours is approximately -0.592 milligrams/meter per hour.

When calculating the rate of change in the concentration of a drug after 1.3 hours, we need to first take the derivative of the concentration function C(t) with respect to time (t). The derivative of C(t) is denoted as C'(t).

By taking the derivative of the given function C(t) = 2.1te^-1.3t with respect to t, we get:

C'(t) = 2.1e^-1.3t (1 - 1.3t)

Substitute t = 1.3 into the derivative formula to find the rate of change specifically at 1.3 hours:

C'(1.3) = 2.1e^-1.3(1.3) (1 - 1.3(1.3))

Calculating this expression gives us C'(1.3) ≈ -0.592 milligrams/meter per hour, which represents the rate of change in the drug concentration after 1.3 hours.

Understanding the rate of change in drug concentration over time is essential for monitoring the effectiveness and impact of the drug within the body. By utilizing mathematical functions and derivatives, we can determine how fast the drug concentration is changing at specific time intervals.