Large corporate office orders 800 novel electronic door locks for the building, but they buy them from the discount supplier. On the day of installation, all 800 of locks are in working order. Though, after 4 weeks, only 784 of locks still work. Let L(t) give number of working locks t weeks after installation and suppose L(t) follows the exponential model.
(a) Determine the function L(t):
(b) Find how many locks still be operational after eight weeks?
(c) Find how many weeks will it be be until there are merely 120 locks still working?