To find the value of \( A(8) \) using the equation \( A(t) = 6(2)^{0.25t} \), we will substitute \( t = 8 \) into the equation.
First, we simplify the exponent:
\[ A(8) = 6(2)^{0.25 \cdot 8} = 6(2)^{2} \]
Next, we calculate \( (2)^2 \):
\[ (2)^2 = 4 \]
Now we substitute this value back into the equation:
\[ A(8) = 6 \cdot 4 = 24 \]
Therefore, the number of bugs after 8 days is 24.