Infectious disease outbreak size If 99$\%$ of a population is initially uninfected and each initial infected person generates, on average, two new infections, then, according to the model we considered in Example 3.5 .13 ,

$$0.99 e^{-2 A}=1-A$$

where $A$ is the fraction of the population infected at the endof an outbreak. Use Newton's method to obtain an approximation (accurate to two decimal places) for the percentage of the population that is eventually infected.