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.

Answer

Step 1 of 3</p>

Uncertainty is the experiments best estimate of how far an experimental value might be from the true value

The frequency in 20 years old men estimated to be 17.71.7 per DNA

The frequency in 40 years old men estimated to be 35.95.8 per DNA

Let m1 is the frequency at age t1

Let m2 is the frequency at age t2

Step 2 of 3</p>

a)The yearly rate of increase is estimated by r=(m2 - m1 )/( t2- t1)

=(35.9-17.7)/(40-20)

=0.91

The uncertainty in the increase is (35.95.8)-(17.71.7)

=(35.9-17.7)(5.8-1.7)

=18.24.1