The half life of a certain tranquilizer in the bloodstream is 42 hours. How long will it take for the drug to decay to 88% of the original dosage?

Question

Need some help thank you and have a good rest of your day/evening/night

Answer 1

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

 

0.88a₀ = a₀(0.5)^t/42        substitute values

0.88 = (0.5)^t/42           divide both sides by a₀

ln 0.88 = ln (0.5)^t/42       take ln of both sides

-0.12783 ≈ (t/42)(-0.6931) calculate

0.1844 ≈ t/42           divide both sides by -0.6931

7.7461 ≈ t              multiply both sides by 42