The average annual cost of college at 4-year private colleges was $34,740 in the 2017–2018 academic year. This was a 3.6% increase from the previous year. 

(a) If the cost of college increases by 3.6% each year, what will be the average cost of college at a 4-year private college for the 2037–2038 academic year? 

(b) College savings plans, such as a 529 plan, allow individuals to put money aside now to help pay for college later. If one such plan offers a rate of 2% compounded continuously, how much should be put in a college savings plan in 2019 to pay for 1 year of the cost of college at a 4-year private college for an incoming freshman in 2037?