Exponential and Logarithmic Models

Question

At the beginning of an experiment, a scientist has 200 grams of radioactive goo. After 135 minutes, her sample has decayed to 12.5 grams.

The half-life of the goo in minutes is 34Correct  

The amount of goo remaining at time .  200^−0.02054(t)Correct  

How many grams of goo will remain after 14 minutes? 

Answer 1

half life is 34 minutes, 14 minutes is maybe 3/4 life or 150 grams left from 200 grams

1 = 2e^34r divide by 2

1/2 =e^34r take natural logs of both sides

ln(1/2) = 34r divide by 34

r = ln(1/2)/34 = -,02039 but you have -02054, which is close. You could just round off to -.02 = -2% per minute decay rate. the 34 minute half life is probably rounded off to the nearest minute.

A = 200e^-.02(14)

A = 200e^-.28 = about 151.2 grams of goo left after 14 minutes.

But use the other information with 135 minutes and 12.5 grams

12.5 = 200e^135r

12.5/200 = e^135r

ln(0.0625) = e^135r

=2.7726 = 135r

r = -2.7726/135 = -0.020537777= -0.2054 = exactly what you have for the decay rate

A = 200e^-.2054(14) = 150.023 grams of goo left after 14 minutes. Round off to 1 decimal and it's 150.0 grams left