which table represents exponential growth? x y 1 2 2 4 3 6 4 8 x y 1 2 2 4 3 8 4 16 x y 1 2 2 4

Explanation:

Step1: Recall exponential - growth formula

An exponential - growth function has the form $y = ab^{x}$ ($a>0,b > 1$), and the ratio of consecutive $y$ - values for a constant increase in $x$ is a constant greater than 1.

Step2: Check the first table

For the first table: When $x = 1,y = 2$; when $x = 2,y = 4$; when $x = 3,y = 6$; when $x = 4,y = 8$. The ratio of consecutive $y$ - values: $\frac{4}{2}=2$, $\frac{6}{4}=\frac{3}{2}$, $\frac{8}{6}=\frac{4}{3}$. The ratios are not constant, so it is not exponential growth.

Step3: Check the second table

For the second table: When $x = 1,y = 2$; when $x = 2,y = 4$; when $x = 3,y = 8$; when $x = 4,y = 16$. The ratio of consecutive $y$ - values: $\frac{4}{2}=2$, $\frac{8}{4}=2$, $\frac{16}{8}=2$. The ratio of consecutive $y$ - values is a constant ($b = 2$), so it represents exponential growth.

Step4: Check the third table

The third table only has two data - points $(x = 1,y = 2)$ and $(x = 2,y = 4)$. We cannot determine if it is exponential growth with just two points.

Answer:

The second table (with $x$ - values 1, 2, 3, 4 and corresponding $y$ - values 2, 4, 8, 16) represents exponential growth.