Sugar is put into a large quantity of water and the mixture is stirred. After 2 minutes, 50% of the sugar has dissolved. How much longer will it take until 90% of the sugar has dissolved?

Question

anonymous · Answer

Answer is 4.644 mins longer (eg 6.644 minutes total). How to solve?

misty1212 · Answer

and more to the point, how could we know the answer? you got a formula or sommat?

anonymous · Answer

A(t) = A0xe^kt? I'm not sure, my teacher didn't go over this topic that well, so I'm extremely clueless.

mathstudent55 · Answer

Every 2 minutes, half of the sugar dissolves.
Start with 100% undissolved sugar at t = 0
At t = 2 min, 50% is still undissolved. At t = 2, 0.5 is undissolved
At t = 4 min, 25% is still undissolved. At t = 4, 0.5 * 0.5 = 0.25 is undissolved
At t = 6 min, 12.5% is still undissolved. At t = 6, 0.5 * 0.5 * 0.5 = 0.125 is undissolved
At t = x 2-minute periods, 0.5^x is undissolved

0.1 = 0.5^x
log 0.1 = x log 0.5
x = log 0.1/log 0.5
x = 3.3219
Since x is the number of 2-minute periods, the time is
2 * 3.3219 min = 6.6438 minutes

mathstudent55 · Answer

6.6438 minutes is the total time for 90% of the sugar to dissolve. 
The question is how much more time than the 2 minutes will it take, so the answer is 4.638 minutes.

anonymous · Answer

Doesn't the info say that 50% has dissolved? Does it imply that it decreases by half every time?

anonymous · Answer

Yeah, that's what I was thinking.

anonymous · Answer

But wouldn't it completely dissolve by 4 minutes, then? Since it decreased by half the first time. 0.0

mathstudent55 · Answer

If 50% dissolves each 2 minutes, then 50% of the sugar remains undissolved each period.

mathstudent55 · Answer

No.
Each 2 minutes that pass, half of the remaining undissolved sugar dissolves.

anonymous · Answer

Okay. I see.