Question

determine if each table represents a linear function or an exponential function. explain your answer in a meaningful sentence – what is being added, subtracted, or multiplied. 15.

x	f(x)
1	23
2	27
3	31
4	35

16.

x	f(x)
1	15
2	75
3	375
4	1875

Explanation:

Step1: Check Table 15's f(x) differences

$23-19=4$, $27-23=4$, $31-27=4$, $35-31=4$

Step2: Classify Table 15's function

Constant difference means linear function.

Step3: Check Table 16's f(x) ratios

$\frac{15}{3}=5$, $\frac{75}{15}=5$, $\frac{375}{75}=5$, $\frac{1875}{375}=5$

Step4: Classify Table 16's function

Constant ratio means exponential function.

Answer:

1. For table 15: This is a linear function, as each value of $f(x)$ increases by a constant 4 when $x$ increases by 1.
2. For table 16: This is an exponential function, as each value of $f(x)$ is multiplied by a constant 5 when $x$ increases by 1.