Given a set of age nodes \(0=x_0,x_1,\ldots,x_n\) and survival fractions \(1=l(x_0),l(x_1),\ldots,l(x_n)\) the force of mortality over the interval \([x_i,x_{i+1})\) is a constant \(\mu_i\) equal to $$ \mu_i = \frac{-1}{x_{i+1}-x_i} \log\left(\frac{l(x_{i+1})}{l(x_i)}\right) $$ If \(T_n\), person-years lived after \(x_n\), is specified then \(\mu_n\) is given by $$ \mu_n = \frac{l(x_n)}{T_n} $$ otherwise set \(\mu_n=\mu_{n-1}\). The the survival fraction at any age \(x\) is then given by $$ l(x)=l(x_i) e^{-\mu_i (x-x_i)} $$ where \(x \in [x_i,x_{i+1})\) and \(x_{n+1}=\infty\).