Question

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

Answer 1

it is c an exponential decay

Answer 2

ANSWER

An exponential decay


Step-by-step explanation

From the given table, the y-values are

`972,324,108,36,12`


We can observe that,


`(324)/(972) = (108)/(324) = (36)/(108) = (12)/(36) = (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{( (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.