4. A radioactive isotope of plutonium, Pu-238, is used to make thermoelectric power sources for spacecraft. The half-life of Pu-238 is 87.7 years. A space probe was launched in 2012 with 2.0 kg of Pu-238. a) Write a function of the form Q(t) = Qo e -kt to model the quantity Q(t) of Pu-238 that is left t years after 2012. b) If 1.6 kg of Pu-238 is required to power the spacecraft's data transmitter, for how long after launch would scientists be able to retrieve data? (Show your equation and work. Round answer to the nearest year.)