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

𝐴
(
𝑡
)
=
6
(
2
)
0.25
𝑡
can represent the number of bugs. Find the value for A(8)
𝐴
(
8
)
.(1 point)
The number of bugs after 8 days is

Answer 1

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

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

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

3. Substitute this value back into the equation: \[ A(8) = 6(2)^{2} \]

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

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

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