To calculate the number of bugs after 8 days using the given equation \( A(t) = 6(2)^{0.25t} \), we will substitute \( t = 8 \) into the equation.
\[ A(8) = 6(2)^{0.25 \times 8} \]
First, calculate \( 0.25 \times 8 \):
\[ 0.25 \times 8 = 2 \]
Now substitute this back into the equation:
\[ A(8) = 6(2)^{2} \]
Next, calculate \( (2)^{2} \):
\[ (2)^{2} = 4 \]
Now substitute this value back into the expression for \( A(8) \):
\[ A(8) = 6 \times 4 \]
Now complete the multiplication:
\[ A(8) = 24 \]
Therefore, the number of bugs after 8 days is \( \boxed{24} \).
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