Question

level k > aa.7 write linear, quadratic, and exponential functi you have prizes to reveall go to your game board. video qu an look at this table: x y 1 3 2 9 3 27 4 81 5 243 write a linear (y = mx + b), quadratic (y = ax²), or exponential (y = a(b)ˣ) function that models the data. y =

Explanation:

Step1: Identify function type

Check ratios of consecutive $y$-values:
$\frac{9}{3}=3$, $\frac{27}{9}=3$, $\frac{81}{27}=3$, $\frac{243}{81}=3$. Constant ratio means exponential.

Step2: Find $b$ (growth factor)

The constant ratio is $b=3$.

Step3: Find $a$ (initial value)

Use $x=1, y=3$ in $y=a(b)^x$:
$3=a(3)^1$
$a=\frac{3}{3}=1$

Step4: Form the function

Substitute $a=1, b=3$ into $y=a(b)^x$.

Answer:

$y=3^x$