How does $$ g(t)=\frac{4}{7^{t}} $$ change over the interval from $$ t=7 $$ to $$ t=8 $$ ? $$ g(t) $$ increases by 7 $$ g(t) $$ decreases by 7 $$ g(t) $$ decreases by a factor of 7 $$ g(t) $$ increases by $$ 7 \% $$

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1. We evaluate the function at $$ t=7 $$ and $$ t=8 $$:
   $$
   g(7)=\frac{4}{7^7}, \quad g(8)=\frac{4}{7^8}=\frac{4}{7^7}\cdot\frac{1}{7}
   $$

2. Notice that
   $$
   g(8)=\frac{1}{7}\,g(7)
   $$
   which means that $$ g(t) $$ is multiplied by $$ \frac{1}{7} $$ when $$ t $$ increases from 7 to 8.

3. Since multiplying by $$ \frac{1}{7} $$ results in a decrease by a factor of 7, we conclude that:
   $$
   g(t) \text{ decreases by a factor of } 7.
   $$
$$ g(t) $$ decreases by a factor of 7.

How does change over the interval from to ?
increases by 7
decreases by 7
decreases by a factor of 7
increases by

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How does change over the interval from to ? increases by 7 decreases by 7 decreases by a factor of 7 increases by