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