Answer
Model:$\quad P=2.56(1.01641)^{t}$ billion people
Work Step by Step
Exponential models have the form: $P=Ab^{t}$
Given the points on the graph
$(0,2.56)\quad\Rightarrow\quad\left\{\begin{array}{l}
2.56=Ab^{0}\\
A=2.56\\
P=2.56b^{t}
\end{array}\right.$
$(61,6.91) $, which is 61 years after 1950 - $\left\{\begin{array}{l}
6.91=2.56b^{61}\\
b^{61}=6.91/2.56\\
b=(6.91/2.56)^{1/61}\\
b\approx 1.01641128142\\
b\approx 1.01641
\end{array}\right.$
Thus, we have the model:
$\quad P=2.56(1.01641)^{t}$ billion people
