To complete the table and find the correct plotted points for the situation, we first need to calculate the value of the home at the end of each year for 5 years using the provided formula:
\[ f(x) = 375,000(1.06)^x \]
We'll compute the home value for \(x = 0\) to \(x = 5\).
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For \(x = 0\): \[ f(0) = 375,000(1.06)^0 = 375,000 \cdot 1 = 375,000 \]
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For \(x = 1\): \[ f(1) = 375,000(1.06)^1 = 375,000 \cdot 1.06 = 397,500 \]
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For \(x = 2\): \[ f(2) = 375,000(1.06)^2 = 375,000 \cdot 1.1236 \approx 422,850 \]
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For \(x = 3\): \[ f(3) = 375,000(1.06)^3 = 375,000 \cdot 1.191016 \approx 446,757 \]
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For \(x = 4\): \[ f(4) = 375,000(1.06)^4 = 375,000 \cdot 1.26247696 \approx 472,559 \]
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For \(x = 5\): \[ f(5) = 375,000(1.06)^5 = 375,000 \cdot 1.338225 \approx 501,090 \]
Now let's summarize the computed values:
| Years (x) | Home Value (f(x)) | |-----------|---------------------| | 0 | 375,000 | | 1 | 397,500 | | 2 | 422,850 | | 3 | 446,757 | | 4 | 472,559 | | 5 | 501,090 |
Now let's verify which graph best represents the increasing home value over time.
The correct description of the function we derived indicates that the values are increasing, not decreasing.
From the response options given, the first option:
An increasing curve with an arrow on the top is plotted on a coordinate plane. The x-axis for years ranges from 0 to 7 in increments of 1. The y-axis for home value ranges from 350,000 to 550,000 in increments of 25,000.
This option describes an increasing curve which matches our computed values for the home value over time, making it the correct choice.
Thus, the answer is: The first graph option.
1 answer