Question
Finish creating the input-output table for the function f(x) = 20(3)^x.
Answers
GPT-4o mini
To create an input-output table for the function \( f(x) = 20(3)^x \), we will calculate the value of \( f(x) \) for several different values of \( x \).
Here is the completed input-output table for selected integer values of \( x \):
| \( x \) | \( f(x) = 20(3)^x \) |
|---------|----------------------|
| -2 | \( f(-2) = 20(3)^{-2} = 20 \times \frac{1}{9} = \frac{20}{9} \approx 2.22 \) |
| -1 | \( f(-1) = 20(3)^{-1} = 20 \times \frac{1}{3} = \frac{20}{3} \approx 6.67 \) |
| 0 | \( f(0) = 20(3)^0 = 20 \times 1 = 20 \) |
| 1 | \( f(1) = 20(3)^1 = 20 \times 3 = 60 \) |
| 2 | \( f(2) = 20(3)^2 = 20 \times 9 = 180 \) |
| 3 | \( f(3) = 20(3)^3 = 20 \times 27 = 540 \) |
The computed outputs correspond to the specified input values. You can add more values of \( x \) to further extend the table if necessary.
Here is the completed input-output table for selected integer values of \( x \):
| \( x \) | \( f(x) = 20(3)^x \) |
|---------|----------------------|
| -2 | \( f(-2) = 20(3)^{-2} = 20 \times \frac{1}{9} = \frac{20}{9} \approx 2.22 \) |
| -1 | \( f(-1) = 20(3)^{-1} = 20 \times \frac{1}{3} = \frac{20}{3} \approx 6.67 \) |
| 0 | \( f(0) = 20(3)^0 = 20 \times 1 = 20 \) |
| 1 | \( f(1) = 20(3)^1 = 20 \times 3 = 60 \) |
| 2 | \( f(2) = 20(3)^2 = 20 \times 9 = 180 \) |
| 3 | \( f(3) = 20(3)^3 = 20 \times 27 = 540 \) |
The computed outputs correspond to the specified input values. You can add more values of \( x \) to further extend the table if necessary.