Question

Which description matches the function represented by the values in this table?

Answer 1

ANSWER

An exponential decay


EXPLANATION

From the given table, the y-values are
$972,324,108,36,12$


We can observe that,

$\frac{324}{972} = \frac{108}{324} = \frac{36}{108} = \frac{12}{36} = \frac{1}{3}$


This is an exponential function and since the absolute value of the common ratio is less than 1, it is an exponential decay.


The formula for this function is,

$y = 972{( \frac{1}{3}) }^{x - 1}$


$y = 972{( 3) }^{ - (x - 1)}$

or

$y = 2916{(3 })^{ - x }$

This function is of the form

$y = a {b}^{kx}$
Since
$k = - 1 \: < \: 0$
is an exponential decay function

The correct answer is C.

Answer 2

it is c an exponential decay