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

I believe you need to first determine the exponential function that fits for the situation. I used 160 as the y-intercept and the "point" (19, 134) to find the growth rate to be .9907. Thus, I have the exponential equation: A(t)=160(.9907)^t

Then, substitute 30 grams in for the amount (A) and solve for time (t) using logs. I got 179.16 days.

Please let me know if you need further assistance, Shelle :)

Answer 2

134/160= e^19r

r= ln(67/80)/19=-.009333369225

30/160=

3/16=e^-.009333369225t

take natural logs of both sides

ln(3/16)= -.009333369225t

t=ln(3/16)/-.009333369225= 179.3539282 days

= about 6 months