Our universe has an age to ~ 13.7 gyr and h. 67.74 km s-1 mpc-1. (a) show that the hubble time is 14.44 gyr and that to = 0.949h,. (b) show that the universe would be 1.42 times younger if it were always matter-dominated (c) show that the universe would be 1.9 times younger if it were always radiation-dominated (d) use the above to argue that radiation-dominated universes expand faster than matter-dominated ones (e) imagine our universe had a single component, show that, to get to = 13.7 gyr, w = -0.300. what kind of universe is this?