Use the table to answer the question.
0 375,000
1
2
3
4
5 The Diaz family purchased a home for $375,000. They decide to sell their home five years later. If the value of the home is increasing at a rate of 6% each year, the situation can be modeled using the equation f(x)=375,000(1.06)x
Finish the table to determine which graph displays the correct plotted points for the situation.(1 point)
Responses
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.
Image with alt text: 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.
An increasing curve with an arrow on the top is plotted on a coordinate plane. The x-axis is labeled Years and ranges from 350,000 to 550,000 in increments of 25,000. The y-axis is labeled Home Value and ranges from 0 to 7 in increments of 1.
Image with alt text: An increasing curve with an arrow on the top is plotted on a coordinate plane. The x-axis is labeled Years and ranges from 350,000 to 550,000 in increments of 25,000. The y-axis is labeled Home Value and ranges from 0 to 7 in increments of 1.
A decreasing curve with an arrow at the end 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 0 to 350,000 in increments of 50,000.
Image with alt text: A decreasing curve with an arrow at the end 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 0 to 350,000 in increments of 50,000.
A decreasing curve with an arrow at the end 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 200,000 to 500,000 in increments of 25,000.
Image with alt text: A decreasing curve with an arrow at the end 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 200,000 to 500,000 in increments of 25,000.
To complete the table, we need to find the value of the home for each of the missing years (1 through 4) using the given exponential growth model f(x) = 375,000(1.06)^x, where x represents the number of years.
For year 1:
f(1) = 375,000 * (1.06)^1 = 375,000 * 1.06 = 397,500
For year 2:
f(2) = 375,000 * (1.06)^2 = 375,000 * 1.122 = 420,750
For year 3:
f(3) = 375,000 * (1.06)^3 = 375,000 * 1.191 = 446,625
For year 4:
f(4) = 375,000 * (1.06)^4 = 375,000 * 1.262 = 473,550
Now, we will complete the table with the computed values:
| x (Year) | f(x) (Home Value) |
|----------|-------------------|
| 0 | 375,000 |
| 1 | 397,500 |
| 2 | 420,750 |
| 3 | 446,625 |
| 4 | 473,550 |
| 5 | ... (not computed) |
To answer the question about the graph, we are looking for an increasing curve since the home value is increasing each year due to the 6% annual growth rate.
The correct description of the graph displaying the situation should be:
- An increasing curve with an arrow on the top, plotted on a coordinate plane.
- The x-axis should be labeled "Years" and range from 0 to at least 5 or beyond (increments are not specified in the question).
- The y-axis should be labeled "Home Value" and include values that range from the initial value of $375,000 to values higher than the computed value for year 4 (at least $473,550).
The provided descriptions of the graphs do not include enough detail about the data points to determine which is correct. However, using the description above, we can rule out any graphs showing a decreasing curve or incorrectly labeled axes since the home value is increasing and the axes labels are important for correctly interpreting the graph. The first description seems to match our criteria for the correct graph, but without seeing the data points, it is challenging to be certain. The second description is incorrect because the axes are labeled in reverse. The third and fourth descriptions are clearly incorrect as they describe a decreasing curve.