The? half-life of a certain substance is 24 years. How long will it take for a sample of this substance to decay to 70?% of its original? amount?

Question

How do you set this up?

Answer 1

A = a₀(0.5)^t/h, a₀ = starting amount, h = half life, t = time.

 

0.7a₀ = a₀(0.5)^t/24               substitute values

0.7 = (0.5)^t/24                     divide both sides by a₀

ln 0.7 = ln (0.5)^t/24              take ln of both sides

-0.3567 ≈ (t/24)(-0.6931)   calculate

0.5146 ≈ t/24                      divide both sides by -0.6931

12.35 ≈ t                             multiply both sides by 24

Answer 2

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