Question

At the beginning of an experiment, a scientist has 176 grams of radioactive goo. After 165 minutes, her sample has decayed to 5.5 grams.

What is the half-life of the goo in minutes?

Find a formula for G(t) , the amount of goo remaining at time t.G(t)=?

How many grams of goo will remain after 50 minutes?

Answer 1

ick goo

Answer 2

you want to solve
\[(\frac{5.5}{176})^{\frac{t}{160}}=\frac{1}{2}\] for t

Answer 3

sorry should be
\[(\frac{5.5}{176})^{\frac{t}{165}}=\frac{1}{2}\]

Answer 4

or maybe
\[0.03125^{\frac{t}{165}}=.5\] to work this with decimals. we get
\[\frac{t}{165}=\frac{\ln(.5)}{\ln(.03125)}\] and so
\[t=\frac{165\ln(.5)}{\ln(.03125)}\]

Answer 5

whatever this is, it is your half life

Answer 6

by some miracle this is a whole number, it is 33

Answer 7

and so your formula is (if you don't like the one i wrote above)
\[G(t)=176\times (\frac{1}{2})^{\frac{t}{33}}\] and now you can replace t by whatever number you like