Let's analyze the function [tex]\( g(t) = 0.35^t \)[/tex] and determine how it changes over the interval from [tex]\( t = 9 \)[/tex] to [tex]\( t = 10 \)[/tex].
1. Calculate [tex]\( g(9) \)[/tex]:
[tex]\[
g(9) = 0.35^9 \approx 7.881563867187496 \times 10^{-5}
\][/tex]
2. Calculate [tex]\( g(10) \)[/tex]:
[tex]\[
g(10) = 0.35^{10} \approx 2.7585473535156234 \times 10^{-5}
\][/tex]
3. Determine the change in value from [tex]\( t = 9 \)[/tex] to [tex]\( t = 10 \)[/tex]:
[tex]\[
\text{Change} = g(10) - g(9) \approx 2.7585473535156234 \times 10^{-5} - 7.881563867187496 \times 10^{-5} \approx -5.123016513671872 \times 10^{-5}
\][/tex]
4. Calculate the percentage change:
[tex]\[
\text{Percentage change} = \left( \frac{\text{Change}}{g(9)} \right) \times 100 \approx \left( \frac{-5.123016513671872 \times 10^{-5}}{7.881563867187496 \times 10^{-5}} \right) \times 100 \approx -65\%
\][/tex]
Based on these calculations, [tex]\( g(t) = 0.35^t \)[/tex] decreases by 65% over the interval from [tex]\( t = 9 \)[/tex] to [tex]\( t = 10 \)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{\text{g(t) decreases by 65 \%}} \][/tex]
