00:01
Hi there, in this question, the initial amount is given as 5 ,000 because in the formula we have a of t, which is 5 ,000 times e to the power 0 .08 t.
00:13
So the initial amount, which is 5 ,000.
00:16
So what we want, we just double this one.
00:19
So the double a, which is 10 ,000.
00:23
So let me just plug in this value here, which is 10 ,000, which is equal to 5 ,000 times e to the power 0 .08.
00:32
Let's simplify this which is 2 is equal to e to the power 0 .08t let's take the ln of each side so the ln2 which is equal to then e to the power 0 .08t that means this is 0 .08t times ln e so the ln e so the ln e is 1 so we got ln2 which is equal to 0 .08 times t so if i just leave t alone, which is 100 times l2 divided by 2, divided by 8.
01:06
So we can get the value of t from this equation and which is.
01:10
So from here, the answer from the calculator, we got 8 .66.
01:16
So after 8 .66 years, that means after 9 years.
01:23
So after 9 years...