To determine the value of the Diaz family's home after 5 years, we can use the equation you provided:
\[ f(x) = 375,000 \times (1.06)^x \]
where \( x \) is the number of years. To find the value of the home after 5 years, we will substitute \( x = 5 \) into the equation:
\[ f(5) = 375,000 \times (1.06)^5 \]
Now let's calculate \( (1.06)^5 \):
\[ (1.06)^5 \approx 1.338225 \]
Now, we multiply this value by $375,000:
\[ f(5) \approx 375,000 \times 1.338225 \approx 501,090.75 \]
Therefore, the approximate value of the home after 5 years is $501,090.75.
Completing the Table
If you have a table to fill out, it might include values for different years. Here’s how the values would look:
| Year (x) | Value of Home (f(x)) | |----------|----------------------------------| | 0 | $375,000 | | 1 | $375,000 * (1.06) ≈ $397,500 | | 2 | $375,000 * (1.06)^2 ≈ $420,450 | | 3 | $375,000 * (1.06)^3 ≈ $444,873 | | 4 | $375,000 * (1.06)^4 ≈ $470,489 | | 5 | $375,000 * (1.06)^5 ≈ $501,090.75|
Graphing the Results
When plotting this on a graph, the x-axis would denote the number of years (0 to 5), and the y-axis would represent the value of the home. You would plot the points corresponding to the values shown above, especially for year 5 (0, 501090.75).
Make sure to choose the graph that correctly displays the increasing trend, with the value at year 5 being approximately $501,090.75.
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