Complete the table, rounding to the nearest thousandths, for the function represented by the graph f(x)=2.25(0.75)x

Question

(3 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
x f(x)
0 Response area
1 Response area
3 Response area

Answer 1

To complete the table for the function \( f(x) = 2.25(0.75)^x \), we will calculate the values of \( f(x) \) for \( x = 0 \), \( x = 1 \), and \( x = 3 \).

1. For \( x = 0 \): \[ f(0) = 2.25(0.75)^0 = 2.25(1) = 2.25 \]

2. For \( x = 1 \): \[ f(1) = 2.25(0.75)^1 = 2.25(0.75) = 1.6875 \]

3. For \( x = 3 \): \[ f(3) = 2.25(0.75)^3 = 2.25(0.421875) \approx 0.948 \]

Now, we will round the results to the nearest thousandths:

• \( f(0) = 2.250 \)
• \( f(1) = 1.688 \) (rounded from 1.6875)
• \( f(3) = 0.948 \)

Here is the completed table:

| x | f(x) | |------|----------| | 0 | 2.250 | | 1 | 1.688 | | 3 | 0.948 |