At the beginning of an experiment, a scientist has 260 grams of radioactive goo. After 240 minutes, her sample has decayed to 4.0625 grams. What is the half-life of the goo in minutes?

Question

I got t=44.1837

however I plug into equation and its wrong?

What am I doing wrong?

Answer 1

Amount remaining in t minutes = A(t) = 260e^kt

4.0625 = 260e^240k

0.015625 = e^240k

ln(0,015625) = 240k

So, k = -0.0173287

A(t) = 260e^-0.0173287t

130 = 260e^-0.0173287t

0.5 = e^-0.0173287t

t = ln(0.5) / (-0.0173287) = 40 minutes

Answer 2

Hi Samantha,

For this problem, first let's calculate the number of half-lives to achieve that remaining amount of the radiactive goo after 240 minutes. To do this,

amount remaining = initial amount * (1/2)^ n

where n = number of half-lives for the decay

4.0625 = 260 * (1/2) ^ n

0.015625 = (1/2)^ n

Solving for n, we will get n = 6 (can use log conversion to solve this)

Note, the decay happened in 240 minutes

Thus, number of half-lives for decay = time for decay / original half-life of goo

original half life = 240 min / 6

= 40 mins

I hope this helps. Kindly feel free to reach out to schedule any tutoring sessions on this subject and others.

Do have a good rest of your day.