18. 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
responses
0.785
1.266
0.949
1.25
1.375
1.274
0.978
0.712
2.25
1.688

Answer 1

To calculate \( f(x) = 2.25(0.75)^x \) for each of the given values of \( x \), we can substitute those values into the function and round the results to the nearest thousandth. Let's compute \( f(x) \) for each specified \( x \) value:

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

2. When \( x = 1 \): \[ f(1) = 2.25(0.75)^1 = 2.25(0.75) = 1.6875 \approx 1.688 \]

3. When \( x = 3 \): \[ f(3) = 2.25(0.75)^3 = 2.25(0.421875) \approx 0.94921875 \approx 0.949 \]

Now we can fill in the table based on our calculations:

| \( x \) | \( f(x) \) | |-----------|---------------| | 0 | 2.25 | | 1 | 1.688 | | 3 | 0.949 |

Completed Table

• For \( x = 0 \): 2.25
• For \( x = 1 \): 1.688
• For \( x = 3 \): 0.949

These values correspond to the responses you provided.