For some genetic mutations, it is thought that the

QUESTION:

For some genetic mutations, it is thought that the frequency of the mutant gene in men increases linearly with age. If \(m_{1}\) is the frequency at age \(t_{1}\), and \(m_{2}\) is the frequency at age \(t_{2}\), then the yearly rate of increase is estimated by \(r=\left(m_{2}-m_{1}\right) /\left(t_{2}-t_{1}\right)\). In a polymerase chain reaction assay, the frequency in 20-year-old men was estimated to be \(17.7 \pm 1.7\) per \(\mu \mathrm{g}\) DNA, and the frequency in 40-year-old men was estimated to be \(35.9 \pm 5.8\) per \(\mu \mathrm{g}\) 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.

Equation Transcription:

Text Transcription:

m_1

t_1

m_2

t_2

r = (m_2 - m_1)/(t_2 - t_1)

17.7 pm 1.7

mu g

35.9 pm 5.8