How does $$ g(x)=4 \cdot 2^{x} $$ change over the interval from $$ x=7 $$ to $$ x=8 $$ ? $$ g(x) $$ decreases by $$ 2 \% $$ $$ g(x) $$ increases by $$ 2 \% $$ $$ g(x) $$ increases by 2 $$ g(x) $$ increases by $$ 100 \% $$

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1. Calculate $$ g(7) $$:
   $$
   g(7) = 4 \cdot 2^7 = 4 \cdot 128 = 512.
   $$

2. Calculate $$ g(8) $$:
   $$
   g(8) = 4 \cdot 2^8 = 4 \cdot 256 = 1024.
   $$

3. Determine the absolute change from $$ x=7 $$ to $$ x=8 $$:
   $$
   \Delta g = g(8) - g(7) = 1024 - 512 = 512.
   $$

4. Calculate the percentage increase:
   $$
   \text{Percentage Increase} = \frac{\Delta g}{g(7)} \times 100\% = \frac{512}{512} \times 100\% = 100\%.
   $$

Thus, $$ g(x) $$ increases by $$ 100\% $$ from $$ x=7 $$ to $$ x=8 $$.
$$ g(x) $$ increases by $$ 100\% $$ from $$ x=7 $$ to $$ x=8 $$.

How does change over the interval from to ?
decreases by
increases by
increases by 2
increases by

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