Question

Finish creating the input-output table for the function: f(x) = 20(3)^x

Answer 1

To create an input-output table for the function \( f(x) = 20(3)^x \), we can choose a range of input values for \( x \) and calculate the corresponding outputs.

Here's a sample table with selected values for \( x \):

| \( x \) | \( f(x) = 20(3)^x \) |
|---------|-----------------------|
| -2 | \( 20(3)^{-2} = 20 \times \frac{1}{9} \approx 2.22 \) |
| -1 | \( 20(3)^{-1} = 20 \times \frac{1}{3} \approx 6.67 \) |
| 0 | \( 20(3)^0 = 20 \times 1 = 20 \) |
| 1 | \( 20(3)^1 = 20 \times 3 = 60 \) |
| 2 | \( 20(3)^2 = 20 \times 9 = 180 \) |
| 3 | \( 20(3)^3 = 20 \times 27 = 540 \) |

So, the complete input-output table would look like this:

| \( x \) | \( f(x) \) |
|---------|-------------|
| -2 | \( \approx 2.22 \) |
| -1 | \( \approx 6.67 \) |
| 0 | 20 |
| 1 | 60 |
| 2 | 180 |
| 3 | 540 |

Feel free to ask for more values or further explanations!