Question 108374
Exponential function
{{{N(t)=N[0]e^(kt)}}}
{{{k=0.018/year}}}
{{{N[0]=2556518868}}}
a.){{{N(t)=2556518868e^(0.018t)}}}
Linear function
b.) {{{F(t)=mt+b}}}
{{{m = (F[2]-F[1])/(t[2]-t[1])}}}
{{{m = (1650-350)/(1980-1950)}}}
{{{m = 1300/30}}}
{{{m = 130/3}}}
Pick one of your values to determine b
{{{1650=(130/3)(1980)+b}}}
{{{b=84150}}}
{{{F(t)=(130/3)t-84150}}}
where t is the year and F(t) is billions kg. 
c.){{{t=1976-1950=26}}}
{{{N(t)=2556518868e^(0.018(26))}}}
{{{N(t)=2556518868e^(0.468))}}}
{{{N(t)=2556518868(1.5967974))}}}
{{{N(t)=4082242688}}}
N(1976) = 4.1 billion (4,082,242,688) humans
{{{F(t)=(130/3)t-84150}}}
{{{F(1976)=(130/3)1976-84150}}}
{{{F(1976)=(130/3)1976-84150}}}
{{{F(1976)=85627-84150}}}
{{{F(1976)=1477}}}
F(1976)=1477 billion kg
d.) Assuming the exponential population model is still valid,
{{{t=2007-1950=57}}}
{{{N(t)=2556518868e^(0.018(57))}}}
{{{N(t)=2556518868e^(1.026)}}}
{{{N(t)=2556518868(2.789884)}}}
{{{N(t)=7132390958}}}
N(2007) = 7.1 billion (7,132,390,958) humans