Desert Samaritan Hospital in Mesa, Arizona, keeps records of its emergency-room traffic. Beginning at 6:00 P.M. on any given day, the elapsed time, in hours, until the first patient arrives is a variable with density curve y = 6.9e−6.9x for x > 0, and y = 0 otherwise. Here e is Euler's number, which is approximately 2.71828. Most calculators have an e-key. Using calculus, it can be shown that the area under this density curve to the left of any number x greater than 0 equals 1 − e−6.9x.
a. Graph the density curve of this variable.
b. What percentage of the time does the first patient arrive between 6:15 P.M. and 6:30 P.M.?