To find the value of \( A(8) \), we will plug \( t = 8 \) into the given equation:
\[ A(t) = 6(2)^{0.25t} \]
Substituting \( t = 8 \):
\[ A(8) = 6(2)^{0.25 \times 8} \]
Calculating \( 0.25 \times 8 \):
\[ 0.25 \times 8 = 2 \]
Now we substitute back into the equation:
\[ A(8) = 6(2)^{2} \]
Calculating \( (2)^{2} \):
\[ (2)^{2} = 4 \]
Now we can multiply by 6:
\[ A(8) = 6 \times 4 = 24 \]
Therefore, the number of bugs after 8 days is \( \boxed{24} \).
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