Exponential Functions

An exponential model has the form $y = a \cdot b^t$ . Two numbers tell the whole story:

$a$ — the initial value: the amount at $t = 0$ (every base raised to the $0$ power is $1$ ).
$b$ — the growth or decay factor: rewrite it as $1 \pm r$ to read the percent rate. If $b = 1 + r$ it's growth (e.g. $1.05 \to 5\%$ up); if $b = 1 - r$ it's decay (e.g. $0.75 \to 25\%$ down — not $75\%$ ).

This is the companion to Linear vs. Exponential: there you decide which model fits; here you read what an exponential model's numbers mean. These are real, released Regents questions.

Question 1 of 30

Exponential models — initial value

The value of a diamond ring, in dollars,

t

years after it is purchased is modeled by

v(t) = 500(1.08)^t

. What was the original price of the ring, in dollars?

$108$460$500$540

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For teachers

Standard, common misconceptions, and suggested use will live here.