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How does changing the time exponent to $\frac{t}{k}$ affect an exponential model $f(t) = a \cdot b^{t/k}$?

デッキ「Digital SAT Math: Algebra, Advanced Math & Geometry」の単語カード。

解答

The value multiplies by factor $b$ every $k$ units of time (e.g., $f(t) = 100(2)^{t/3}$ doubles every 3 hours).

解説

Digital SAT questions frequently ask to convert annual growth rates to monthly rates: $(1 + r)^t = ((1 + r)^{1/12})^{12t}$, where the monthly growth factor is $(1 + r)^{1/12}$.

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