Discrete change and recurrence models

Model discrete change with first-order recurrences in this precalculus practice set. Translate repeated losses, additions, percentage changes and scheduled updates into mathematical rules. Work with initial states, net changes, fixed values and boundaries where a simple model would otherwise predict an impossible quantity.

The questions develop from reading an update rule to calibrating unknown parameters and comparing discrete and continuous descriptions. Single-select and multiselect tasks include detailed explanations of operation order, indexing, units and assumptions. Use exact arithmetic unless a question specifies otherwise. The examples are simplified mathematical models, not claims about actual tanks, inventory systems or populations. General recurrence theory is outside the scope; later sequence and series sets develop the special additive and multiplicative structures.