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 outputs (f(x)) for several chosen input values (x). Here’s how you can fill out the table:
| \( x \) | \( f(x) = 20(3)^x \) |
|---------|----------------------|
| 0 | \( 20(3)^0 = 20(1) = 20 \) |
| 1 | \( 20(3)^1 = 20(3) = 60 \) |
| 2 | \( 20(3)^2 = 20(9) = 180 \) |
| 3 | \( 20(3)^3 = 20(27) = 540 \) |
| 4 | \( 20(3)^4 = 20(81) = 1620 \) |
| 5 | \( 20(3)^5 = 20(243) = 4860 \) |
### Summary of the table:
- For \( x = 0 \), \( f(0) = 20 \)
- For \( x = 1 \), \( f(1) = 60 \)
- For \( x = 2 \), \( f(2) = 180 \)
- For \( x = 3 \), \( f(3) = 540 \)
- For \( x = 4 \), \( f(4) = 1620 \)
- For \( x = 5 \), \( f(5) = 4860 \)
This table shows how the output \( f(x) \) increases exponentially as the input \( x \) increases.
| \( x \) | \( f(x) = 20(3)^x \) |
|---------|----------------------|
| 0 | \( 20(3)^0 = 20(1) = 20 \) |
| 1 | \( 20(3)^1 = 20(3) = 60 \) |
| 2 | \( 20(3)^2 = 20(9) = 180 \) |
| 3 | \( 20(3)^3 = 20(27) = 540 \) |
| 4 | \( 20(3)^4 = 20(81) = 1620 \) |
| 5 | \( 20(3)^5 = 20(243) = 4860 \) |
### Summary of the table:
- For \( x = 0 \), \( f(0) = 20 \)
- For \( x = 1 \), \( f(1) = 60 \)
- For \( x = 2 \), \( f(2) = 180 \)
- For \( x = 3 \), \( f(3) = 540 \)
- For \( x = 4 \), \( f(4) = 1620 \)
- For \( x = 5 \), \( f(5) = 4860 \)
This table shows how the output \( f(x) \) increases exponentially as the input \( x \) increases.