To find the value of \( A(8) \) using the equation \( A(t) = 6(2)^{0.25t} \), we need to substitute \( t = 8 \) into the equation.
So, we have:
\[ A(8) = 6(2)^{0.25 \times 8} \]
Calculating the exponent:
\[ 0.25 \times 8 = 2 \]
Now substitute back into the equation:
\[ A(8) = 6(2)^{2} \]
Calculating \( (2)^{2} \):
\[ (2)^{2} = 4 \]
Now substitute that back in:
\[ A(8) = 6 \times 4 \]
Finally, multiplying gives:
\[ A(8) = 24 \]
Therefore, the number of bugs after 8 days is 24.