Equation and estimate amount algebra help needed

Question

A radioactive isotope has a half life of 1,920 years let f(t) be the amount of isotope,in milligrams, that is present after t years. If the sample originally contained 21 milligrams, write an equation modeling this situation.

-F(t) = ___

Estimate the amount of isotope remaining after 3,558 years. Round your answer to three decimal places. __ mg

Answer 1

The half-life formula is N(t) = N₀(1/2)^t/t_(1/2) where:

N(t) = quantity of the substance remaining <-- what we need to determine

N₀ = initial quantity of the substance = 21 mg

t = time elapsed = 3558 years

t_1/2 = half-life of the substance = 1920 years

N(t) = N₀(1/2)^t/t_(1/2) = 21(1/2)^3558/1920 ≈ 5.813

Therefore, there will be 5.813 mg of the sample left after 3558 years.

Hope this helped!