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?

Answer 1

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.