Question

73 grams of a substance decays to 60 after 10 hours

a) determine the half life of the substance and b) how long it takes the substance to decay to 12 grams.

Answer 1

Calculator and formulas may be found here:
http://www.1728.org/halflife.htm

Part a)
half-life = elapsed time * log(2) / log (begng amt/ending amt)
half-life = 10 hrs * 0.3010299957 / log (73/60)
half-life = 10 hrs * 0.3010299957 / log (1.2166666667)
half-life = 10 hrs * 0.3010299957 / 0.0851716097
half-life = 35.3439336408 hours

Part b)
time = half-life * log(bgng amt/ending amt) / log (2)
time = 35.343936408 hours * log(73/12)/ 0.3010299957
time = 35.343936408 hours * log(6.0833333333)/ 0.3010299957
time = 35.343936408 hours * 0.7841416141/ 0.3010299957
time = 92.0660789274 hours

Yes, it's just that simple! :-)