radioactive element decays

Question

A radioactive element decays into non-radioactive substances. In 840840 days the radioactivity of a sample decreases by 6262 percent. Give your answer to the following questions round to the nearest whole number of days.

(a) What is the half-life of the element?

half-life:    (days)

(b) How long will it take for a sample of 100100 mg to decay to 6060 mg?

time needed:    (days)

Answer 1

A=Pe^rt

t= time in days

r = rate of change per day

P=original amount

A =ending amount after t days

(1-.62) = e^840r

ln.38 = 840r

r = ln.38/840= about -.00115=- 0.115% per day

half life is when

A/P = .5 = e^rt =e^(ln.38/840)t

ln.5 = tln.38/840

t = 840ln.5/ln.38

= about 601.75 days = half life

100 to 60 takes t which satisfies

60/100 = e^(ln.38/840)t

t = 840ln.6/ln.38

= about 443.47 days