A quantity with an initial value of 830 grows exponentially at a rate such that the quantity doubles every 2 weeks. What is the value of the quantity after 21 days, to the nearest hundredth?
To find the value of the quantity after 21 days, we first need to determine how many doubling periods occur within 21 days.
Since the quantity doubles every 2 weeks, it will double 21 days / 14 days = 1.5 times.
Therefore, the final value of the quantity after 21 days is 830 * 2^1.5 = 830 * 2^0.5 ≈ 830 * 1.414 ≈ 1174.42
Therefore, the value of the quantity after 21 days is approximately 1174.42 to the nearest hundredth.