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
can represent the number of bugs. 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 will substitute \( t = 8 \) into the equation.

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

Calculating \( 0.25 \times 8 \):

\[
0.25 \times 8 = 2
\]

Now substitute this back into the equation:

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

Now compute \( (2)^2 \):

\[
(2)^2 = 4
\]

Now substitute that in:

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

Thus, the value for \( A(8) \) is \( \boxed{24} \).