Population growth and doubling time

Study population growth and doubling time through carefully specified exponential models. This precalculus set focuses on calibrating a growth law from observations, interpreting multiplicative change, translating between continuous rate and periodic growth factor, and calculating when a population reaches a target.

Tasks include observations away from time zero, comparisons between populations, changes of time origin and the effect of altering a growth rate. Single-select and multiselect questions ask you to connect algebraic results to the meaning of the model. The examples are synthetic or explicitly idealized; the calculations do not claim that every population follows unrestricted exponential growth.

Review logarithms, exponential equations, ratios and units before starting. Use exact expressions unless a numerical approximation is requested. Worked explanations show how to divide observations to remove the initial-value parameter, identify the elapsed time and check the fitted model against the given data. The authored sequence develops from direct interpretation to calibration and comparison, while each question remains self-contained. Pay particular attention to the difference between the population at the chosen origin and a later observed count, and to the assumptions needed before extrapolating beyond the observation interval.