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

Question

asked Dec 10, 2022 140k views

2 Answers

Andrew Dunaway · Answer 1 · 2022-12-16T23:33:14+0000

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.