Question $3$: Let's estimate how differences in the measurement of the expansion rate of the universe $($ h $0)$ will affect the estimation of the age of the universe. To do this we need to know, the distance the universe has expanded $($d$)$ and the rate$/$velocity of the expansion $(H_0(d)).$ Then you can use the normal formula to calculate time from a distance and velocity. Hint: do you need to know the value of $($d$)$ to solve for the age?

In $2018,$ the Plank mission released a measurement of $H_0$ as $67\mathrm{.}66k\frac{m}{s}\frac{?}{Mpc}.$ In $2020,$ the SH$0$ES collaboration released a measurement of $74\mathrm{.}03k\frac{m}{s}\frac{?}{Mpc}.$ What is the age of the universe for each measurement of $H_0?$