Answer fully with work

5. Moderna is distributing COVID-19 vaccines, but based on their projections, as they produce more vaccines there will be less demand and so the rate at which they distribute vaccines will decrease, On July 1, 2021 they were distributing vaccines at a rate of 10 million per month. Moderna models that the rate of distribution is decreasing exponentially at a continuous rate, and that each month they will distribute half of what they distributed the previous month. (a) (4 points) Assuming that Moderna's model is correct, how many vaccines will Moderna have distributed between July 1, 2021 and December 31. 2021? Moderna will have distributed million vaccines between July 1 and December 31 (b) (4 points) Assuming that Moderna's model stays correct forever. how many vaccines will Mod- erna distribute after July 1, for the rest of time? After July 1, Moderna will distribute million vaccines