Question

current attempt in progress let ( g(t) ) give the market value (in $1000s) of a house in year ( t ). what does the statement ( g(5) - g(0) = 20 ) tell you about the house? the average house’s market value between years ( t = 0 ) and ( t = 5 ) was $20,000. the house’s market value increased 20 times between years ( t = 0 ) and ( t = 5 ). the house’s market value increased by $20,000 between years ( t = 0 ) and ( t = 5 ). the house’s market value decreased by $20,000 between years ( t = 0 ) and ( t = 5 ). the average rate of change of the house’s market value was $20,000 per year between years ( t = 0 ) and ( t = 5 ). etextbook and media hint save for later attempts: 0 of 5 used submit answer

Explanation:

• \( g(t) \) is the market value in $1000s. So \( g(5)-g(0) = 20 \) means the change in value is \( 20\times1000=\$20,000 \).
• It represents the difference in value between year 5 and year 0, so it's the increase (since the result is positive) in market value between \( t = 0 \) and \( t = 5 \).
• The first option is wrong as it refers to average value, not the difference. The second is wrong as it's not a multiple but a difference. The fourth is wrong as the result is positive (increase, not decrease). The fifth is wrong as average rate of change would be \( \frac{g(5)-g(0)}{5 - 0} \), not \( g(5)-g(0) \).

Answer:

C. The house’s market value increased by $20,000 between years \( t = 0 \) and \( t = 5 \).