Question

To obtain the sequence 1, 1/3, 1/9, 1/27,..., what domain should be applied to the exponential function shown here?

Answer 1

Consider the exponential function

$y=\left(\dfrac{1}{3}\right)^x.$

• At x=0, $y=\left(\dfrac{1}{3}\right)^0=1;$
• At x=1, $y=\left(\dfrac{1}{3}\right)^1=\dfrac{1}{3};$
• At x=2, $y=\left(\dfrac{1}{3}\right)^2=\dfrac{1}{9};$
• At x=3, $y=\left(\dfrac{1}{3}\right)^3=\dfrac{1}{27};$
• and so on.

Thus, the domain is {0, 1, 2, 3, ...}

Answer: option D.