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