the half-life of a certain substance is 28 years. How long will it take for a sample of this substance to decay to 71% of it's original amount?

Answer 1

t = years

A₀ = initial amount

A(t) = amount remaining after t years

The exponential decay law for this problem is

A(t) = A₀ (0.5)^t/28

Set A(t)=71, A₀=100, and solve for t.

71 = 100 (0.5)^t/28

0.71 = (0.5)^t/28

log(0.71) = (t/28) log0.5

You should be able to finish from here.