To complete the table and determine which graph correctly represents the scenario given, we need to calculate the home values for each year based on the model \( f(x) = 375,000(1.06)^x \).
Let's compute the values for \( x \) from 0 to 5:
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When \( x = 0 \): \[ f(0) = 375,000(1.06)^0 = 375,000(1) = 375,000 \]
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When \( x = 1 \): \[ f(1) = 375,000(1.06)^1 = 375,000(1.06) = 397,500 \]
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When \( x = 2 \): \[ f(2) = 375,000(1.06)^2 = 375,000(1.1236) \approx 421,350 \]
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When \( x = 3 \): \[ f(3) = 375,000(1.06)^3 = 375,000(1.191016) \approx 446,257 \]
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When \( x = 4 \): \[ f(4) = 375,000(1.06)^4 = 375,000(1.26247696) \approx 472,859 \]
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When \( x = 5 \): \[ f(5) = 375,000(1.06)^5 = 375,000(1.338225) \approx 501,091 \]
Now, we can summarize the values in the table:
\[ \begin{array}{|c|c|} \hline x & f(x) \ \hline 0 & 375,000 \ 1 & 397,500 \ 2 & 421,350 \ 3 & 446,257 \ 4 & 472,859 \ 5 & 501,091 \ \hline \end{array} \]
Now that we have the completed values, let's summarize them:
- At year 0: $375,000
- At year 1: $397,500
- At year 2: $421,350
- At year 3: $446,257
- At year 4: $472,859
- At year 5: $501,091
Pay attention to the description of the graphs:
- Increasing curve - This would reflect the positive growth in home value.
- Decreasing curve - This would reflect a decline in home value.
Since the value of the home is increasing at a rate of 6% per year, the correct graph that corresponds to this data is the increasing curve.
Therefore, the correct response is the graph that shows an increasing curve on a coordinate plane for the home values over time.