Question

What is the decay factor of the exponential function
represented by the table?

Answer 1

Explanation:

2

Answer 2

Given:

The table of values of an exponential function.

To find:

The decay factor of the exponential function.

Solution:

The general form of an exponential function is:

`y=ab^x` ...(i)

Where, a is the initial value and
`0<b<1` is the decay factor and
`b>1` is the growth factor.

The exponential function passes through the point (0,6). Substituting
`x=0,y=6` in (i), we get

`6=ab^0`

`6=a(1)`

`6=a`

The exponential function passes through the point (1,2). Substituting
`x=1,y=2,a=6` in (i), we get

`2=6(b)^1`

`2=6b`

`(2)/(6)=b`

`(1)/(3)=b`

Here,
`b=(1)/(3)` lies between 0 and 1. Therefore, the decay factor of the given exponential function is
`(1)/(3)`.

Hence, the correct option is A.