Question

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Martin purchased a condo below market value in 2001. He paid $92,500 for the condo even though the market value of the condo was much higher. In 2014, Martin transferred to another city for work and had to sell his condo. The market value of his condo increased over time, as shown in the graph below, where the y-axis represents the market value of the condo, in dollars, and the x-axis represents the number of years since 2001.

Graph shows a curve plotted in quadrant 1 of a coordinate plane. The X-axis is labeled years since 2001 and the Y-axis is labeled market value in dollars. The curve begins at (0, 100000) and exponentially rises through (9, 160000) and (13, 200000).

The initial market value of the condo is $
.


The percent increase per year of the market value of the condo is
%.


The interval on which Martin owned the condo is
≤ x ≤
.

Answer 1

The initial market value of the condo was $100,000. The percent increase per year in market value is approximately 6.67%. Martin owned the condo from 2001 to 2014, hence the interval is 0 ≤ x ≤ 13.

Step-by-step explanation:

The student has been asked to determine the initial market value of a condo, the annual percent increase in the market value, and the interval during which Martin owned the condo. By analyzing the given graph, we can see that the curve starts at a point corresponding to the year 2001 on the x-axis and has a market value on the y-axis of $100,000. This indicates the initial market value of the condo.

To determine the percent increase per year, we look at the market value at a later point in time on the graph. For example, after 9 years (in 2010), the market value of the condo was $160,000. Considering the initial value was $100,000, we can calculate the percent increase using the following formula:

• Percent Increase = ((New Value - Original Value) / Original Value) × 100

• Percent Increase = (($160,000 - $100,000) / $100,000) × 100

• Percent Increase = 60%

Dividing the total percent increase by the number of years gives the annual percent increase:

• Annual Percent Increase = Total Percent Increase / Number of Years

• Annual Percent Increase = 60% / 9 years

• Annual Percent Increase = Approximately 6.67%

Martin owned the condo from 2001 to 2014; therefore, the interval can be expressed as 0 ≤ x ≤ 13, where x represents the years since 2001.