## Intermediate Algebra for College Students (7th Edition)

The world population in 2080 will be $1.38\times 10^{10}$.
2010 world population was approximately = $6.9 \times 10^{9}$ Let $x$ = 2080 world population According to the problem 2010 world population will double in 2010. Thus, $x = 2\times(6.9 \times 10^{9})$ Recall the multiplication of numbers in scientific notation: $(a\times10^{n})(b\times10^{m}) = (a\times b) \times 10^{n+m}$ Thus, $x = 2\times(6.9 \times 10^{9})$ can be rewritten as $x = (2\times 10^{0})\times(6.9 \times 10^{9})$ $x = (2\times 6.9)\times 10^{0+9}$ $x = 13.8\times 10^{9}$ In scientific notation, the numerical factor must be between 1 and 10; hence $x = 13.8\times 10^{9}$ can be rewritten as: $$x = 1.38\times 10^{10}$$