Question

At the beginning of 2000, Ryan's house was worth 234 thousand dollars, and Mark's house was worth 124 thousand dollars. At the beginning of 2003, Ryan's house was worth 182 thousand dollars, and Mark's house was worth 150 thousand dollars. Assume that the values of both houses vary at exponential rates. What can be inferred about the trend in the values of Ryan's and Mark's houses?

a) Both houses increased in value exponentially.

b) Both houses decreased in value exponentially.

c) Ryan's house increased, while Mark's house decreased in value exponentially.

d) Ryan's house decreased, while Mark's house increased in value exponentially.

Answer 1

Ryan's house decreased in value from $234,000 to $182,000 while Mark's house increased in value from $124,000 to $150,000 between 2000 and 2003, indicating that Ryan's house's value decreased exponentially and Mark's house's value increased exponentially.

Step-by-step explanation:

The question involves evaluating the change in value of two houses owned by Ryan and Mark over a period from 2000 to 2003. To infer the trend in the values of Ryan's and Mark's houses, we need to compare the initial values of their houses in 2000 with their values in 2003.

Ryan's house was worth $234,000 in 2000 and $182,000 in 2003. This shows a decrease in value. In contrast, Mark's house was worth $124,000 in 2000 and became $150,000 in 2003, indicating an increase in value. Therefore, we can conclude that Ryan's house decreased in value exponentially, while Mark's house increased in value exponentially.

So, the correct answer to the student's question is: d) Ryan's house decreased, while Mark's house increased in value exponentially.