Question

World Population Growth After its fastest rate of growth ever during the 1980s and 1990s, the rate of growth of world population is expected to slow dramatically in twenty-first century. The function G() - 1.58 -0.2136 gives the projected annual average percent population growth per decade in theith decade, with corresponding to 2000 (a) What will the projected annual average population growth rate be in 2030 ( 47(Round your answer to two decimal places.) % per decade 17(Round your answer to two decimal places.) (b) How fast will the projected annual average population growth rate be changing in 2010 ( % per decade per decade

Answer 1

We are given equation for growth rate

$G(t)=1.58e^{-0.213t}$

(A)

we can plug t=4

$G(4)=1.58e^{-0.213(4)}$

$G(4)=0.67$..........Answer

(B)

$G(t)=1.58e^{-0.213t}$

we can find derivative

$G'(t)=1.58(-0.213)e^{-0.213t}$

now, we can plug t=4

$G'(4)=1.58(-0.213)e^{-0.213(4)}$

$G'(4)=-0.14$.............Answer