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