Final answer:
To find the value of the quantity after 6 weeks, calculate the number of 9-day periods and use the growth rate formula. The value after 6 weeks is approximately 8083.
Step-by-step explanation:
To find the value of the quantity after 6 weeks, we first need to calculate the number of 9-day periods in 6 weeks. There are 6 weeks * 7 days/week = 42 days in 6 weeks. Since each 9-day period represents a growth rate of 75%, we can calculate the number of 9-day periods as 42 days / 9 days = 4.67 periods. Since we can't have a fraction of a period, we can round this down to 4 periods.
Next, we can calculate the final value of the quantity. For each 9-day period, the quantity grows by 75%. So after 1 period, the quantity will be 860 * (1 + 0.75) = 1505. After 2 periods, the quantity will be 1505 * (1 + 0.75) = 2633. After 3 periods, it will be 2633 * (1 + 0.75) = 4619. After 4 periods, it will be 4619 * (1 + 0.75) = 8083.
Therefore, after 6 weeks, the value of the quantity will be approximately 8083, rounded to the nearest hundredth.