Question

look at this table:

x	y
2	20
3	40
4	80
5	160

write a linear ($y = mx + b$), quadratic ($y = ax^2$), or exponential ($y = a(b)^x$) function that models the data.
$y = \square$

Explanation:

Step1: Identify function type

Check ratios of consecutive $y$-values:
$\frac{20}{10}=2$, $\frac{40}{20}=2$, $\frac{80}{40}=2$, $\frac{160}{80}=2$. Constant ratio means exponential.

Step2: Find $a$ (initial value)

When $x=1$, $y=10$. Use $y=a(b)^x$, substitute $x=1$, $y=10$, $b=2$:
$10 = a(2)^1$
$a = \frac{10}{2}=5$

Step3: Write final function

Substitute $a=5$, $b=2$ into $y=a(b)^x$.

Answer:

$y=5(2)^x$