To complete the table and determine which graph displays the correct plotted points for the situation, we will calculate the home value for each year from 0 to 5 using the given equation \( f(x) = 375,000(1.06)^x \).
Here are the calculations:
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For \( x = 0 \): \[ f(0) = 375,000(1.06)^0 = 375,000 \times 1 = 375,000 \]
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For \( x = 1 \): \[ f(1) = 375,000(1.06)^1 = 375,000 \times 1.06 = 397,500 \]
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For \( x = 2 \): \[ f(2) = 375,000(1.06)^2 = 375,000 \times 1.1236 \approx 422,750 \]
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For \( x = 3 \): \[ f(3) = 375,000(1.06)^3 = 375,000 \times 1.191016 \approx 446,187 \]
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For \( x = 4 \): \[ f(4) = 375,000(1.06)^4 = 375,000 \times 1.26247696 \approx 472,357 \]
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For \( x = 5 \): \[ f(5) = 375,000(1.06)^5 = 375,000 \times 1.33822576 \approx 502,648 \]
Now, we can fill in the table:
\[ \begin{array}{|c|c|} \hline \text{Years (x)} & \text{Home Value (f(x))} \ \hline 0 & 375,000 \ 1 & 397,500 \ 2 & 422,750 \ 3 & 446,187 \ 4 & 472,357 \ 5 & 502,648 \ \hline \end{array} \]
Now, let's analyze the graphs provided:
- The graph must be increasing since the home value increases over time.
- The correct y-axis range for home values must include all calculated values, which are between 375,000 and approximately 502,648, so it should be between 350,000 and at least above 500,000.
Based on the attributes of the graphs presented, the correct graph is:
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 graph matches the appropriate criteria for the situation described.
1 answer