A quantity with an initial value of 990 grows exponentially at a rate such that the quantity doubles every 4 years. What is the value of the quantity after 0.7 decades, to the nearest hundredth?
Since 1 decade is 10 years, 0.7 decades is 0.7 * 10 = 7 years.
Since the quantity doubles every 4 years, after 7 years, it will have doubled (7 / 4) times.
Thus, the final value of the quantity is 990 * (2^(7/4)) = 990 * (2^1.75) ≈ 990 * 3.97 ≈ 3924.3.
Therefore, the value of the quantity after 0.7 decades is 3924.3 to the nearest hundredth. Answer: \boxed{3924.30}.