Question

9
which of the following table of values is an exponential function? (a.fgr.9.5)
a

x	y
2	12
3	6
4	3

b

x	y
3	12
4	25
5	50

c

x	y
3	16
4	25
5	36

d

x	y
4	7
6	13
8	19

Explanation:

Step1: Recall exponential function property

An exponential function $y = ab^x$ (where $b>0, b
eq1$) has a **constant ratio** between consecutive $y$-values when $x$ increases by 1.

Step2: Test Option A

Calculate ratios of consecutive $y$-values:
$\frac{12}{24} = \frac{1}{2}$, $\frac{6}{12} = \frac{1}{2}$, $\frac{3}{6} = \frac{1}{2}$
All ratios are equal to $\frac{1}{2}$.

Step3: Verify other options (elimination)

• Option B: $\frac{12}{6}=2$, $\frac{25}{12}\approx2.08$, $\frac{50}{25}=2$ → Ratios are not constant.
• Option C: $\frac{16}{9}\approx1.78$, $\frac{25}{16}=1.5625$, $\frac{36}{25}=1.44$ → Ratios are not constant.
• Option D: $\frac{7}{1}=7$, $\frac{13}{7}\approx1.86$, $\frac{19}{13}\approx1.46$ → Ratios are not constant.

Answer:

A.

x	y
2	12
3	6
4	3