Question

The number of bugs doubles every 4 days. If the bug population starts with 6 bugs then the equation A (t) = 6(2)^0.25t. Find the value for A (8)

Answer 1

To find the value of \( A(8) \) using the equation \( A(t) = 6(2)^{0.25t} \), we simply substitute \( t = 8 \) into the equation:

\[
A(8) = 6(2)^{0.25 \times 8}
\]

Calculating \( 0.25 \times 8 \):

\[
0.25 \times 8 = 2
\]

Substituting this back into the equation:

\[
A(8) = 6(2)^2
\]

Now, calculate \( (2)^2 \):

\[
(2)^2 = 4
\]

So now we can substitute again:

\[
A(8) = 6 \times 4 = 24
\]

Thus, the value of \( A(8) \) is:

\[
\boxed{24}
\]