Question

The projected population of a certain ethnic​ group(in millions) can be approximated by ​p(t)equals=39.63 left parenthesis 1.026 right parenthesis Superscript t39.63(1.026)t where tequals=0 corresponds to 2000 and 0<t<50

The projected population of a certain ethnic​  group(in

millions) can be approximated by ​p(t) equals= 39.63 left parenthesis 1.026 right parenthesis Superscript t 39.63 ( 1.026 )t where t equals= 0 corresponds to 2000 and 0 less than or equals t less than or equals 50 0≤t≤ 50 .a. Estimate the population of this group for the year 2010.b. What is the instantaneous rate of change of the population when t equals= ​ 10?

Answer 1

The equation is
p(t) = 39.63 (1.026)^t
At 2010, t = 10
Solving for p
p(10) = 36.63 (1.026)^10
p(10) = 47.35 million
The instantaneous rate of change is
dp/dt when t=10 = 1.11 million/year