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) .(1 point)

Question

The number of bugs after 8 days is .

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.

Start with the equation: $$A(t)=6(2{)}^{0.25t}$$

Substituting $t=8$: $$A(8)=6(2{)}^{0.25\cdot 8}$$

Calculating $0.25\cdot 8$: $$0.25\cdot 8=2$$

Now, substitute this back into the equation: $$A(8)=6(2{)}^2$$

Calculating $(2{)}^2$: $$(2{)}^2=4$$

Now, multiply by 6: $$A(8)=6\cdot 4=24$$

Therefore, the number of bugs after 8 days is $\boxed{{\displaystyle 24}}$.