Question

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

Answer 1

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
 Answer:
 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
 Answer:
 the instantaneous rate of change of the population when tequals 10 is:
 1.17202555