Question

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


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Answer 1

To complete the table for the function \( f(x) = 2.25(0.75)^x \), we need to calculate \( f(x) \) for the given values of \( x \). We'll round to the nearest thousandths.

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

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

3. For \( x = 3 \):
\[
f(3) = 2.25(0.75)^3 = 2.25(0.421875) \approx 0.950
\]

Now we can fill in the table with the rounded values:

| x | f(x) |
|-------|----------|
| 0 | 2.250 |
| 1 | 1.688 |
| 3 | 0.950 |

So the completed table for \( f(x) = 2.25(0.75)^x \) is as follows:

- For \( x = 0 \): \( f(0) = 2.250 \)
- For \( x = 1 \): \( f(1) = 1.688 \)
- For \( x = 3 \): \( f(3) = 0.950 \)