How does $$ g(x)=3^{x} $$ change over the interval from $$ x=0 $$ to $$ x=1 $$ ? $$ g(x) $$ decreases by a factor of 3 $$ g(x) $$ increases by $$ 200 \% $$ $$ g(x) $$ decreases by $$ 3 \% $$ $$ g(x) $$ increases by 3

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We evaluate the function at the endpoints:

1. At $$ x=0 $$:
   $$
   g(0)=3^0=1
   $$

2. At $$ x=1 $$:
   $$
   g(1)=3^1=3
   $$

The change from $$ g(0) $$ to $$ g(1) $$ is from 1 to 3. The new value is 3 times the original value. To express this as a percentage increase, we calculate:
$$
\text{Percentage increase} = \frac{g(1)-g(0)}{g(0)} \times 100\% = \frac{3-1}{1} \times 100\% = 200\%
$$

Thus, $$ g(x) $$ increases by $$200\%$$ over the interval from $$ x=0 $$ to $$ x=1 $$.
$$ g(x) $$ increases by $$200\%$$ over the interval from $$ x=0 $$ to $$ x=1 $$.

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

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