A radioactive substance has a half-life of 20 days.

a) How much time is required so that only

of the original amount remains?

b) Find the rate of decay at this time.

My attempts:

a) Since after 20 days the substance decays by half of its mass, after 40 days it decays to

, and after 60 days it decays to

. After 80 days it decays to

of its original mass and after 100 days it decays to

of its original mass. Therefore, it will take 100 days for the substance to decay to [tex]\frac{1}{32}/MATH] of its original mass.

b)

is the rate of decay when

days.

I just wanted to know if my answers are correct? I checked with derivative calculators and they have given me very different answers for b. Thanks in advance.