For some genetic mutations, it is thought that the frequency of the mutant gene in men increases linearly with age. If m₁ is the frequency at age t₁, and m₂ is the frequency at age t₂, then the yearly rate of increase is estimated by r = (m₂ − m₁)/(t₂ − t₁). In a polymerase chain reaction assay, the frequency in 20-year-old men was estimated to be 17.7 ± 1.7 per μg DNA, and the frequency in 40-year-old men was estimated to be 35.9 ± 5.8 per μg DNA. Assume that age is measured with negligible uncertainty.

a. Estimate the yearly rate of increase, and find the uncertainty in the estimate.

b. Find the relative uncertainty in the estimated rate of increase.