A 45 gram sample of a substance that's used to preserve fruit and vegetables has a k-value of 0.1109.

Find the substances half-life in days. Round your answer to the nearest tenth.

The decay formula is

N (t) = N₀ exp (-kt)

where

N₀ = 45 g, original mass

N (t) = mass after time t, days

k = 0.1109, the decay constant.

At half life, N (t) = (1/2) * N₀. Therefore

1/2 = exp (-0.1109t)

Take natural log of each side.

ln (0.5) = - 0.1109t

t = ln (0.5) / (-0.1109) = 6.25 days

Answer: 6.3 days (nearest tenth)

The decay formula is

N (t) = N₀ exp (-kt)

where

N₀ = 45 g, original mass

N (t) = mass after time t, days

k = 0.1109, the decay constant.

At half life, N (t) = (1/2) * N₀. Therefore

1/2 = exp (-0.1109t)

Take natural log of each side.

ln (0.5) = - 0.1109t

t = ln (0.5) / (-0.1109) = 6.25 days

Answer: 6.3 days (nearest tenth)