The half-life of cesium-137 is 30 years. Suppose we have a 16-g sample (a) Find

Question

The half-life of cesium-137 is 30 years. Suppose we have a 16-g sample (a) Find a function m(t) mo2-th that models the mass remaining after t years m(t)16-2 (b) Find a function m(t) = moe-t that models the mass remaining after t years. (Round your r value to four decimal places.) m(t)23e Hl (c) How much of the sample will remain after 86 years? (Round your answer to one decimal place.) 9 d) After how many years will only 2 g of the sample remain? (Round your answer to the nearest whole number.) yr

Explanation / Answer

Ans b: 16e-0.0231t

r = 0.693 / 30 = 0.0231

Ans c: 2.19458 g

N = N0e-rt = 16e-0.0231(86) = 2.19458

Ans d: 117.23161 years

t = (1/r) ln(N0/N) = 1/0.0231 ln (30/28) = 117.23161

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