Question

Which sequence is modeled by the graph below? points are (1,3) (2,0.6) (3, 0.12)

Answer 1

ANSWER
$a_n =3( \frac{1}{5} ) ^{n - 1}$
Step-by-step explanation

The ordered points given to us are
$(1,3),(2,0.6),(3,0.12)$
The y-coordinates are the terms in the sequence.

We use the y-coordinates to determine the common ratio.

$r = \frac{0.6}{3} = \frac{0.12}{0.6} = \frac{1}{5}$

The first term of the sequence is the first y-coordinate.

$a_1 = 3$

The nth term of an exponential sequence is given by,



$a_n =a_1 \times r ^{n - 1}$


We now substitute the above values in to the general formula to obtain,


$a_n =3( \frac{1}{5} ) ^{n - 1}$

Answer 2

A) works for all three sets of ordered pairs.