Problem

Assess a periodic first model for a compound-interest account with a fixed positive rate and \(\text{no}~\text{withdrawals}\). State the judgment, independent variable, behavior over time, existence of a positive period, and the appropriate alternative model.

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A periodic model is yes, exactly. The independent variable is time; any repeatedly scheduled interest payment makes the balance repeat; the period can be any compounding interval; and there are no relevant model limitations.

A periodic model is no. The independent variable is the account balance; the balance changes by a constant amount each year; there is no positive period; and a linear model should be used.

A periodic model is yes. The independent variable is time; each compounding interval returns the balance to an earlier value; the period is 1 year; and a sinusoidal model should be used.

A periodic model is no. The independent variable is time; the balance compounds monotonically rather than returning to prior values; a relevant period is no positive period; and use an exponential growth model.

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Assess a periodic first model for a compound-interest account with a fixed positive rate and \(\text{no}~\text{withdrawals}\). State the judgment, independent variable, behavior over time, existence of a positive period, and the appropriate alternative model.

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