b) Find the time required for the population to triple. 18) The half-life ut Rda

Question

b) Find the time required for the population to triple. 18) The half-life ut Rdai un 226 is 1600 years. Suppose we have a 24 mg sample, tr t sa Find a function m(t)?no 2-that models the mass remaining after t years. a) Find a function m) me that models the mass remaining after t years. b) How much of the sample will still remain after 4000 years? c) After how long will only l6 mg of the sample remain? 15) The half-life of strontium-90 is 14 hrs. How long will it take a 50 mg sample to decay to a mass of 30 mg? 16) Radium-2 2 i has a halflife of 30 seconds. I low long will it take for 90% of a sample to decay?

Explanation / Answer

a) m(t) = mo 2^(-t/h)

m(t) = 24*2^(-t/1600)

b) sample remaining after 4000 years

m(t) = 24*2 ^(-4000/1600)

m(t) = 4.24 mg

sample remaining after 4000 years = 4.24 mg

c) 16 =  24*2^(-t/1600)

dividing both sides by 24

16/24 = 2^(-t/1600)

ln (16/24 ) / ln (2) = -t / 1600

t = 935.94

so, after 936 years sample will be 16 mg

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