A quantity starts at \(300\) and grows \(7\%~\text{yearly}\). Analyze the candidate models \(300\cdot~1.07^{x}\), \(300\cdot~0.07^{x}\), and \(300(1~+~0.07)^{x}\). Identify the equivalent valid models and the invalid model with its error, then calculate both \(\text{one}\text{-}\text{interval}\) predictions.

A percent-growth base must contain both the original whole and the decimal increase. We’ll simplify each candidate factor, identify which expressions are equivalent, and flag any base that uses only the rate as the whole multiplier. Evaluating every candidate after one interval will make the intended growth and any unintended decay unmistakable.