Question

Use the table to answer the question.

Complete the table to determine the corresponding plots and identify the correct graph.
Year Value of Home (in $)
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

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.
▶Click for Long Desc
Image with description 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.

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.
▶Click for Long Desc
Image with description 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.

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.
▶Click for Long Desc
Image with description 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.

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.

Answer 1

First finish the table using f(x) = 375,000(1.06)^x:

- Year 0: 375,000
- Year 1: 397,500 (=375,000·1.06)
- Year 2: 421,350 (=397,500·1.06)
- Year 3: 446,631 (=421,350·1.06)
- Year 4: 473,428.86 (=446,631·1.06)
- Year 5: 501,834.59 (=473,428.86·1.06)

These values increase each year, so the correct graph is the second option: the increasing curve with y-axis from 350,000 to 550,000 (the increasing exponential plot).