Answer:
a) [tex]a(t)= 6.27e^{0.0147*t}[/tex]
b) 6.84 million
c) 2028.52
d) 47 years
Step-by-step explanation:
a)Here we know standard exponential growth rate is
[tex]a(t)= ae^{k*t}[/tex]
In this put t=0 and a(t)=6.27 million
thus we get a = 6.27 million
now [tex]\frac{da}{dt}=a(t)k[/tex]
this is equal to(in 2012)=[tex]\frac{1.47}{100}*=0.0147[/tex]
b)Put t = 6
we get
[tex]a(t)= 6.27e^{0.0147*6}[/tex]
=6.84 million
c) [tex]8 = 6.27e^{0.0147*t}[/tex]
take log both sides
we get 16.52 years
d) [tex]2*6.27=6.27e^{0.0147*t}[/tex]
take log both sides we get 47 years to get double the current population.
