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What is the general model for exponential growth and exponential decay, and what do the parameters represent?

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

解答

$f(t) = a(1 + r)^t = a \cdot b^t$ for growth ($b > 1$, where $r$ is the percent growth rate as a decimal), and $f(t) = a(1 - r)^t = a \cdot b^t$ for decay ($0 < b < 1$).

解説

The parameter $a$ is the initial value at $t = 0$ (the y-intercept), and $b$ is the growth or decay factor per unit time.

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