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

Question

can represent the number of bugs. Find the value for A(8)
.(1 point)
The number of bugs after 8 days is
.

Answer 1

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

Let's do the calculation step-by-step:

1. Substitute \( t = 8 \) into the equation: \[ A(8) = 6(2)^{0.25 \times 8} \]

2. Calculate \( 0.25 \times 8 \): \[ 0.25 \times 8 = 2 \]

3. Now, substitute back into the equation: \[ A(8) = 6(2)^2 \]

4. Calculate \( (2)^2 \): \[ (2)^2 = 4 \]

5. Now, calculate \( A(8) \): \[ A(8) = 6 \times 4 = 24 \]

Thus, the number of bugs after 8 days is \( \boxed{24} \).