Let X be the random variable that represents the number of years a patient with a particular type of cancer survives after receiving radiation therapy. Suppose X has an exponential distribution with parameter k. Research indicates that a patient with this type of cancer has an 80% chance of surviving for at least 5 years after radiation therapy begins.

a. Use this information to determine k.

b. What is the probability of a cancer patient surviving at least 10 years after beginning radiation therapy?