The projected population of a certain ethnic group(in millions) can be approximated by p(t)equals 39.87 left parenthesis 1.016 right parenthesis superscript t where tequals 0 corresponds to 2000 and 0 less than or equals t less than or equals 50 . a. estimate the population of this group for the year 2010. b. what is the instantaneous rate of change of the population when tequals 10

For this case, the first thing we will do is rewrite the function.
 We have then:
 p (t) = (39.87) * (1.016) ^ t
 Part A:
 For t = 10 we have:
 p (10) = (39.87) * (1.016) ^ 10
 p (10) = 46.72865869
 
 The population of this group for the year 2010 is:
 p (10) = 46.72865869
 Part B:
 We must calculate in this case the following expression:
 (1,016) ^ t
 Substituting for t = 10
 (1,016) ^ 10 = 1.17202555
 
 the instantaneous rate of change of the population when tequals 10 is:
 1.17202555