In late March of 2020, it was estimated that the number of cases of COVID-19 in New York state was doubling every 3 days. At the time, the number of cases was estimated to be 26,000.
(a) Assuming that this trend continues, find a function of the form y = y₀(2^t/k), without doing any calculations, that describes the number of COVID-19 cases in New York state in terms of t, the number of days since the above quoted figures.
(b) Assuming that this trend continues, in how many days would the number of COVID-19 cases be greater than the population of New York state of 19.54 million? Discuss whether it is realistic to expect an epidemic to continue at this rate.