00:01
So for this problem, a woman starts with $5 ,700, and we want to determine how much money she will have after three years if it is compounded at a rate of 6 % continuously.
00:11
So that would be a equals your principal, which is $5 ,700 ,000, raised to your rate as a decimal.
00:21
So move that two places to the left, 0 .06 times 3.
00:26
And you would just plug that into your calculator, and that gives you 6 ,824, and 14 cents.
00:59
So b wants to know how long it'll take for it to reach $10 ,000.
01:02
So that's the amount that you're trying to get equals 5 ,700 e to the 0 .06, and we're solving for time.
01:16
So the first thing you do here is divide both sides by 5 ,700.
01:23
It looks like i added an extra zero here, which is 1 .75.
01:41
And then you want to change this into a natural log.
01:43
So the natural log that has a base of e of 1 .75 equals the exponent, 0 .06, and divide both sides by 0 .06.
01:58
So i'm going to go ahead and take this part into my calculator...