Suppose the number-average molecular weight Mn of a biodegradable polymer falls by hydrolysis as Mn(t) = Mn₀exp(−kt). For k = 0.030 day⁻¹, which value is closest to the number of days until Mn falls to 20% of its initial value?

Answer: C. About 54 days

From exp(−kt) = 0.20, t = ln(1/0.20)/k = ln 5/0.030 = 1.609/0.030 ≈ 53.6 days, about 54 days. About 23 days uses the common logarithm log 5 ≈ 0.699 instead of the natural logarithm. About 27 days assumes the molecular weight falls linearly in proportion to time, giving 0.80/0.030. In reality, acid accumulating inside a large part speeds up degradation there and crystallization proceeds during degradation, so the fall deviates from a simple exponential. Also, strength is lost later than the molecular weight falls, and mass loss (resorption) begins even later. For this reason the composition and molecular weight of the material are chosen so that it keeps its strength until the bone heals and is resorbed afterward.