Bot GPT 4-o mini To complete the table for the equation \( f(x) = 375,000(1.06)^x \), we can calculate the home value for each year from 0 to 5:
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For year \( x = 0 \): \[ f(0) = 375,000 \times (1.06)^0 = 375,000 \times 1 = 375,000 \]
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For year \( x = 1 \): \[ f(1) = 375,000 \times (1.06)^1 = 375,000 \times 1.06 = 397,500 \]
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For year \( x = 2 \): \[ f(2) = 375,000 \times (1.06)^2 = 375,000 \times 1.1236 \approx 442,350 \]
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For year \( x = 3 \): \[ f(3) = 375,000 \times (1.06)^3 = 375,000 \times 1.191016 \approx 446,445 \]
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For year \( x = 4 \): \[ f(4) = 375,000 \times (1.06)^4 = 375,000 \times 1.26247696 \approx 474,221 \]
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For year \( x = 5 \): \[ f(5) = 375,000 \times (1.06)^5 = 375,000 \times 1.33822590 \approx 501,090 \]
Now, filling in the values, the completed table is:
\[ \begin{array}{|c|c|} \hline \text{Years (x)} & \text{Home Value (f(x))} \ \hline 0 & 375,000 \ 1 & 397,500 \ 2 & 421,350 \ 3 & 446,445 \ 4 & 474,221 \ 5 & 501,090 \ \hline \end{array} \]
Now we can check each graph option:
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The first option has an x-axis labeled "Years" with values ranging from 350,000 to 550,000, which seems incorrect since it should range from years 0 to 5.
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The second option has the x-axis for years ranging from 0 to 7, and the y-axis for home value ranges from 350,000 to 550,000 in increments of 25,000. This is the correct format according to our calculations.
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The third and fourth options describe decreasing curves which are not applicable, as the home value is increasing over time.
Based on the completed table and analysis, the correct response is the second option, which shows the x-axis for years ranging from 0 to 7 and the y-axis for home value ranging from 350,000 to 550,000.
1 answer