Question

This table shows the input and output values for an exponential function f(x) .

What is the ratio of outputs for any two inputs that are one value apart?



−2
−12
4
2

x −3 −2 −1 0 1 2 3
f(x) −18 −14 −12 −1 −2 −4 −8

Answer 1

The answer should be 4 −8

Answer 2

Answer:

$r=2$

Step-by-step explanation:

1) Rewriting the table below:

(Check the graph below)

2) Inputs( x-values) and the outputs are dependent variables (y).

Picking two points

$(-3,\frac{-1}{8}), (-2,\frac{-1}{4} )$

3) Similarly to a Geometric Sequence. Looking to the f(x) row to find the ratio, we need always to divide the later term over the previous one:

$r=\frac{y_{2}}{y_{1}}=\frac{y_{3}}{y_{2}}=(...)=\frac{y_{n+1}}{y_{n}}$

4) Hence,

$r=\frac{\frac{-1}{4}}{\frac{-1}{8}}\Rightarrow r=\frac{-1}{4}*-8 \Rightarrow r=\frac{-8}{-4}=2$