Answer:
10.8 days (3 sig.figs.)
Step-by-step explanation:
All radioactive decay is 1st order decay defined by the expression A = A₀e^-kt
which is solved for time of decay (t) => t = ln(A/A₀) / -k
A = final weight = 1.0 gram
A₀ = initial weight = 16.0 grams
k = rate constant = 0.693/t(1/2) = 0.693/2.69 days = 0.258 days⁻¹
t = ln(1/16) / -0.258da⁻¹ = (-2.77/-0.258) days = 10.74646792 days (calculator)
≅ 10 days (1 sig. fig. based on given 1 gram mass)