Question

write an exponential function for the table. write the function in the form $y = a(b)^x$.\
\

$x$	$y$	\
---	---	\
1	8	\
2	16	\
3	32	\
4	64

Explanation:

Step1: Find base $b$

Notice that each $y$-value is double the previous one: $\frac{16}{8}=2$, $\frac{32}{16}=2$, $\frac{64}{32}=2$. So $b=2$.

Step2: Solve for $a$

Use $x=1, y=8$ and $b=2$ in $y=a(b)^x$:
$8 = a(2)^1$
$8 = 2a$
$a = \frac{8}{2}=4$

Step3: Verify the function

Check with $x=2$: $y=4(2)^2=4\times4=16$, which matches. Check $x=3$: $y=4(2)^3=4\times8=32$, which matches. Check $x=4$: $y=4(2)^4=4\times16=64$, which matches.

Answer:

$y=4(2)^x$