A scientist models the concentration of a drug in the bloodstream as C(t) = 50 × e^(-0.2t), where t is in hours. What is the concentration after 4 hours?

Thu, 16 Apr 2026 13:36:05 +0000

Understanding Drug Concentration Over Time: A Scientist’s Model Explained When developing new medications, understanding how a drug concentrates in the bloodstream over time is critical for determining effective dosages and ensuring patient safety. One commonly used mathematical model to describe this process is the exponential decay function: C(t) = 50 × e^(-0.2t)
where C(t) represents the drug concentration in the bloodstream at time t (measured in hours), and e is Euler’s mathematical constant (~2.718). This model reflects how drug levels decrease predictably over time after administration—slowing as the body metabolizes and eliminates the substance. In this article, we explore the significance of the formula and, focusing on a key question: What is the drug concentration after 4 hours?