Question

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

A) (0, ∞)
B) [0, ∞)
C) {1, 2, 3, ...}
D) {0, 1, 2, 3, ...}

Answer 1

Consider the exponential function

`y=\left((1)/(3)\right)^x.`

• At x=0,
  `y=\left((1)/(3)\right)^0=1;`
• At x=1,
  `y=\left((1)/(3)\right)^1=(1)/(3);`
• At x=2,
  `y=\left((1)/(3)\right)^2=(1)/(9);`
• At x=3,
  `y=\left((1)/(3)\right)^3=(1)/(27);`
• and so on.

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

Answer: option D.