⚠️ Educational & Entertainment Disclaimer: This interactive tool and associated content are provided for educational, revision, and entertainment purposes only. They do not constitute medical, clinical, or professional pharmaceutical advice, diagnosis, or treatment. Never use mathematical models or online simulators to calculate real-world medical dosages.

Interactive Medicine Dosage & Decay Simulator

Pharmacokinetics is the branch of pharmacology dedicated to determining the fate of substances administered to a living organism. Mathematics—specifically exponential decay and linear modeling—plays a critical role in calculating safe drug dosages, half-lives, and clearance rates in the human bloodstream. Use the simulator below to track how a medication concentration drops over time!

C(t) = 100 × (0.80)^t
Initial Dose: 100 mg Hourly Decay Rate: 20% Concentration after 4h: 40.96 mg

💡 GCSE STEM Teacher Tip: Ask students to calculate how many hours it takes for the drug concentration to drop below a safe therapeutic threshold (e.g., 20 mg).

📄 GCSE STEM Practice Tasks: Maths in Medicine

Name: __________________________      Class: ____________      Date: ____________

Task 1

A patient is administered an antibiotic injection. The concentration of the drug in the bloodstream, C, in milligrams per liter (mg/L), after t hours is modeled by the exponential equation: C = 120 × (0.75)ᵗ

a) What is the initial concentration of the drug in the patient’s bloodstream at t = 0? (1 mark)

b) Calculate the drug concentration exactly 2 hours after injection. (2 marks)

Task 2

Complete the missing values for a painkiller breaking down in the body according to the formula C = 80 × (0.5)ᵗ (half-life model):

Time t (Hours) 0 1 2 3 4
Concentration C (mg/L) 80 40 … 10 …
Task 3

Clinical Application: Why is understanding exponential decay and half-life vital for doctors when prescribing continuous medication dosages to avoid patient toxicity?

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