The painting doubles in value every 7 years and is worth $24,000 at year 21.

Working backward:

• Year 21: $24,000
• Year 14: $12,000
• Year 7: $6,000
• Year 0: $3,000

At year 8 (1 year after year 7), the painting is worth more than $6,000 but has not yet doubled to $12,000. Since only 1 of the 7 years has passed, the value is between $6,000 and $9,000.