Battery life between charges for a certain mobile phone is 20 hours when the primary use is talk time, and drops to 7 hours when the phone is primarily used for Internet applications over a cellular network. Assume that the battery life in both cases follows an exponential distribution. 

a. Show the probability density function for battery life for this phone when its primary use is talk time. 

b. What is the probability that the battery charge for a randomly selected phone will last no more than 15 hours when its primary use is talk time? 

c. What is the probability that the battery charge for a randomly selected phone will last more than 20 hours when its primary use is talk time? 

d. What is the probability that the battery charge for a randomly selected phone will last no more than 5 hours when its primary use is Internet applications?