pre calc question

Question

A scientist begins with a sample of 160 grams of a certain radioisotope. After 19 days, the sample has decayed to 134 grams. How long after the beginning of the process will it take to decay to 30 grams?

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

Answer:  days.

Answer 1

m(t) = 160e^rt; m(19) = 160e^19r = 134; r = ln(134/160)/19 = - 0.00933337; m(t) = 160e^-0.00933337t.

m(t) = 160e^-0.00933337t = 30; t = ln(30/160)/(-0.00933337) = 179.35 days