Question

which table represents an exponential function?

x	f(x)
1	3
2	5
3	8
4	11

x	f(x)
1	4
2	16
3	64
4	256

x	f(x)
1	4
2	6
3	10
4	12

Explanation:

Step1: Define exponential function rule

An exponential function has the form $f(x) = ab^x$, where consecutive $f(x)$ values have a constant multiplicative ratio.

Step2: Check first table

Calculate ratios of consecutive $f(x)$:
$\frac{3}{1}=3$, $\frac{5}{3}\approx1.67$, $\frac{8}{5}=1.6$, $\frac{11}{8}=1.375$. Ratios are not constant.

Step3: Check second table

Calculate ratios of consecutive $f(x)$:
$\frac{4}{1}=4$, $\frac{16}{4}=4$, $\frac{64}{16}=4$, $\frac{256}{64}=4$. Ratios are constant ($4$).

Step4: Check third table

Calculate ratios of consecutive $f(x)$:
$\frac{4}{2}=2$, $\frac{8}{4}=2$, $\frac{10}{8}=1.25$, $\frac{12}{10}=1.2$. Ratios are not constant.

Answer:

The second table (with $x$ values 0,1,2,3,4 and $f(x)$ values 1,4,16,64,256) represents an exponential function.