In 1900, the life expectancy of a newborn child was 46 years, and by 2000, it had grown to 77 years. Over the same century, the life expectancy of a person at age 65 grew from 76 years to 83 years. Both of these life expectancies increased linearly with time between 1900 and 2000.

a. Find the function B(t) that represents the life expectancy of a newborn child t years after 1900 and the function E(t) that represents the life expectancy of a 65-year-old.

b. Sketch the graphs of E(t) and B(t). Then determine the age A to which both a newborn child and a 65-year-old person can expect to live.