To find the value of \( A(8) \) in the equation \( A(t) = 6(2)^{0.25t} \), we will substitute \( t = 8 \).
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Substitute \( t = 8 \) into the equation:
\[ A(8) = 6(2)^{0.25 \times 8} \]
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Calculate \( 0.25 \times 8 \):
\[ 0.25 \times 8 = 2 \]
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Substitute this back into the equation:
\[ A(8) = 6(2)^{2} \]
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Now calculate \( (2)^{2} \):
\[ (2)^{2} = 4 \]
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Substitute that value back into the equation:
\[ A(8) = 6 \times 4 \]
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Finally, calculate \( 6 \times 4 \):
\[ A(8) = 24 \]
Thus, the number of bugs after 8 days is 24.
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