How do I solve M= 88*(1/2)^(t/20) describes the mass in kg of a radioactive material over time in years when will the mass be 11kg?

Question

anonymous · Answer

original mass * 0.5^(timeelapsed/halflife) = mass left

0.5^(ttotal/thalf) = massleft/originalmass

(ttotal/thalf)*log(0.5) = log(massleft/originalmass)
ttotal = (log(massleft/originalmass)*thalf)/log(0.5)

plug in 20 for thalf, 88 for originalmass, and 11 for massleft

anonymous · Answer

you get 60 years

anonymous · Answer

"after 60 years, M of the material will be 11 kg"

anonymous · Answer

Thank you but how do i start?

anonymous · Answer

there's an easier way to solve this problem lol

88 kg is the original mass of the material and the half life of the material is 20 years.

after 1 half life (i.e. after 20 years has elapsed) the material will weight 44 kg

after 2 half lives (40 years elapsed) the mass of the material will be 22 kg

after 3 half lives (60 years elapsed) the material will be 11 kg

anonymous · Answer

ok

anonymous · Answer

Did you plug in for T? im sorry im still a little confused