HSC · Topic explainer
Finding an exponential decay model from two points
In y = kaˣ, k is the value at time zero and a is the factor for one time unit. Divide the later value by the earlier value to remove k. Take the root corresponding to the number of elapsed time units to find a, then substitute a point to determine k.
Worked example
A model records 80 mg at hour two and 20 mg at hour six. The elapsed time is four hours, so a⁴ = 20 ÷ 80 = 0.25. The positive fourth root is √0.5, approximately 0.7071.
Substitute the earlier point. Because a² = 0.5, 80 = 0.5k and k = 160 mg. Check that at hour six the model gives 160 × 0.5³ = 20 mg.
Official exam practice
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