Catalyst. A catalyst is a substance that alters the rate of a chemical reaction without undergoing any permanent change itself.

A chemist, while adding a particular catalyst to a reaction, observes that the time elapsed for the reaction to complete is a variable with density curve y = 2e−2x from x > 0, and y = 0 otherwise. Here e is Euler’s number, which is approximately 2.71828. 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−2x .

a. Graph the density curve of this variable.

b. What percentage of the time does it take to finish 50% of the reaction?