A state's population as a function of time t(in years) is given by
p(t)= 44,178,000+78,000t
and its healthcare costs are given by
c(t) =47,863,00+430,500t +178t^2
a. Create the function representing the state's per capita healthcare costs (i.e.) the average cost per citizen)
b. Find the average rate of change in the per capita healthcare costs from year 5 to 11.