i have the table

t Caffine

0 125

1 111

2 98

3 87

4 77

5 69

6 61

7 54

8 47

9 42

10 38

11 34

12 30

13 26

14 23

15 21

16 18

17 16

18 14

19 13

20 11

21 10

22 9

23 8

24 7

The time is in hours and the caffine is the decrease in milligrams. Doing this in excel, i got the exponential decay formula of y = 124.96e-0.1202t which seems to be correct because if i do it to like 2 hours i get

124.96e^((-0.1202)*2)=98.26, which corresponds to our table showing 98.

Now i wanted to see how long it would take for the caffine to reach 0 milligrams. I am trying to use the example

Problem 2: According to our model, when will the population reach 300 thousand?

To solve this problem we set 100 e0.08t equal to 300 and solve for t.

100 e0.08t = 300

e0.08t = 3 Take the natural logarithm of both sides.

ln e0.08t = ln 3

0.08t = ln 3

t = (ln 3)/0.08 = 13.73, approximately.

Therefore, the population is expected to reach 300 thousand about three fourths of the way through the year 1993.

Obviously this doesnt relate to my problem, but it shows a way to do it. So if i set my formula to 124.96e^((-0.1202)t)=0 this means i would first have to divide both sides by 124.96 which doesnt really work on the side which is 0, cos when i come to take the natural logarithm, i get ln0 which returns an error on my calculator. Any advice on how i can find out when the caffine miligrams will be 0?