pre calc question

Question

A scientist begins with a sample of 200 grams of a certain radioisotope. After 13 days, the sample has decayed to 163 grams. How long after the beginning of the process will it take to decay to 50 grams?

Give your answer in days, rounded to two decimal places.

Answer:  days.

Answer 1

163 = 200e^13r

163/200 = .815 = e^13t

take natural logs of both sides

13t = ln.815

t = ln.815/13 = about -.01574

50 = 200e^-01574(13) = 200e^-.20462

50/200 = 1/4

1/4 = e^-.20462t

take natural logs

-.20462t = ln.25

t= ln.25/-.20462

t = 6.775 x 13 =

t= 88.075 days to reach 50 grams

t = 88.08 days rounded to 2 decimals

= 88 days 4 minutes 57 seconds