a radioactive isotope decays exponentially. if 800 grams decays to 100 grams in 3 hours, how much will be left after 4 hours?

Question

i dont understand how to get the final answer when i find the value of .

Answer 1

Terrance,

 

You model the decay mass  M(t) = M_o e^-ct

where, M(t) is remaining mass at time t, M_o is the starting mass at time zero, and c is the constant of decay.

 

The problem specifies that at t=3 hrs, M(3) = 100g, M_o = 800 g, so we can solve for the single unknown, c.

M(3)/Mo = 100/800 = 0.125 = e^-3c.

So ln_e(0.125) = -2.07944 = -3c,  and c = + 0.693

 

Now at t=4 hours, M(4) = 800 e^-0.693(4) = 800 e^-2.772 = 800 (0.0625) = 47.26 grams