Given equation is
[tex]P=6.4(1.0126)^t[/tex]
It gives approx world population in billions for t years since 2004.
Answer(a):
Compare with growth formula P=a(b)^t, we get:
growth factor b = 1.0126
We know that if r is the percent rate of growth then
1+r=b
1+r=1.0126
r=0.0126
Hence the yearly percent rate of growth of the world population is 0.0126 or 1.26%.
Answer(b):
To find worlds population in 2004, plug t=0 because year is counted from 2004.
[tex]P=6.4(1.0126)^0 = 6.4*1 = 6.40[/tex]
Hence answer is 6.40 billion.
To find worlds population in 2018, plug t=2018-2004=14 because year is counted from 2004.
[tex]P=6.4(1.0126)^{14} = 6.4*1.19160117479 = 7.62624751867[/tex]
Hence answer is approx 7.63 billion.
Answer(c):
Average rate of change of the world population between 2004 and 2018 is given by:
[tex]\frac{P\left(Year_{2018}\right)-P\left(year_{2004}\right)}{2018-2004}[/tex]
[tex]=\frac{P\left(14\right)-P\left(0\right)}{14-0}[/tex]
[tex]=\frac{7.63-6.40}{14}[/tex]
[tex]=0.0878571428571[/tex]
Hence answer is approx 0.0878571428571 billion per year.
To convert it into millions, multiply by 1000
So we get 0.0878571428571*1000 = 87.8571428571
Which is approx 88 to the nearest integer
Hence final answer is approx 88 millions per year.
