Question

Which table represents an exponential function of the form $y=b^x$ when $0<b<1$?

• A.

  

• B.

  

• C.

  

• D.

  

Answer 1

The correct option is B

Explanation for the correct option:

Lets assume the exponent is of the form $y={\left(\frac{1}{3}\right)}^x$

Substituting the values of $x$ we get:

$\begin{array}{rcl}x& =& -3\\ y(-3)& =& {\left(\frac{1}{3}\right)}^{-3}=27\\ x& =& -2\\ y(-2)& =& {\left(\frac{1}{3}\right)}^{-2}=9\\ x& =& -1\\ y(-1)& =& {\left(\frac{1}{3}\right)}^{-1}=3\\ x& =& 0\\ y\left(0\right)& =& {\left(\frac{1}{3}\right)}^0=1\\ x& =& 1\\ y\left(1\right)& =& {\left(\frac{1}{3}\right)}^1=\frac{1}{3}\\ x& =& 2\\ y\left(2\right)& =& {\left(\frac{1}{3}\right)}^2=\frac{1}{9}\\ x& =& 3\\ y\left(3\right)& =& {\left(\frac{1}{3}\right)}^3=\frac{1}{27}\end{array}$

Hence, option(B) is the correct answer.