How does $$ g(t)=\frac{1}{3^{t}} $$ change over the interval from $$ t=1 $$ to $$ t=2 $$ ? $$ g(t) $$ decreases by $$ 3 \% $$ $$ g(t) $$ decreases by 3 $$ g(t) $$ decreases by a factor of 3 $$ g(t) $$ increases by 3

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First, evaluate the function at $$ t = 1 $$ and $$ t = 2 $$:
$$
g(1) = \frac{1}{3^1} = \frac{1}{3}
$$
$$
g(2) = \frac{1}{3^2} = \frac{1}{9}
$$

Next, find the factor change from $$ t = 1 $$ to $$ t = 2 $$ by calculating the ratio:
$$
\frac{g(2)}{g(1)} = \frac{\frac{1}{9}}{\frac{1}{3}} = \frac{1}{9} \times \frac{3}{1} = \frac{1}{3}
$$

This shows that when $$ t $$ increases from $$ 1 $$ to $$ 2 $$, the function value becomes $$\frac{1}{3}$$ of what it was at $$ t = 1 $$. In other words, $$ g(t) $$ decreases by a factor of 3.
$$ g(t) $$ decreases by a factor of 3.

How does change over the interval from to ?
decreases by
decreases by 3
decreases by a factor of 3
increases by 3

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How does change over the interval from to ? decreases by decreases by 3 decreases by a factor of 3 increases by 3