According to a country's census, the number of people (in thousands) who are expected to be over 100 years old in year x is approximated by the functionf(x)=0.27x² +3.54x+50.78, where x = 0 corresponds to the year 2000 and the formula is valid through 2045.(a) Find a formula giving the rate of change in the number of people over 100 years old.(b) What is the rate of change in the number of people expected to be over 100 years old in the year 2015?(c) Is the number of people expected to be over 100 years old increasing or decreasing in 2015?(a) The formula for the rate of change of the number of people over the age of 100 is f'(x) =