Question

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

Answer 1

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

$2=6(b)^1$

$2=6b$

$\dfrac{2}{6}=b$

$\dfrac{1}{3}=b$

Here, $b=\dfrac{1}{3}$ lies between 0 and 1. Therefore, the decay factor of the given exponential function is $\dfrac{1}{3}$.

Hence, the correct option is A.