Exponential and Logarithmic Functions · Paper 3 — Free Maths AI HL Practice Questions

A researcher is studying the population decay of a rare bacterial colony in a controlled laboratory environment. The population $P$ (in thousands of cells) at time $t$ (in days) is modelled by $P(t) = Ae^{-kt}$, where $A$ and $k$ are positive constants. The initial population is $500$ thousand cells. After $10$ days, the population is $250$ thousand cells.