# A small country that had 20 million people in 1990 has experienced exponential growth in population of 4% per year since then. How do you write an equation that models this situation and use your equation to determine when the population will double?

Feb 19, 2016

${P}_{x}$, the population after $x$ years, is given by $20 \cdot {1.04}^{x}$ million and population doubles in $17.67$ years.

#### Explanation:

Population is 20 million people in 1990 and growth in population of 4% per year. Hence, after $x$ years population will be

$20 {\left(1 + \frac{4}{100}\right)}^{x}$ million or $20 \cdot {1.04}^{x}$ million .

Hence, ${P}_{x}$, the population after $x$ years, is given by $20 \cdot {1.04}^{x}$ million.

If it doubles in x years, $20 \cdot {1.04}^{x} = 40$ or ${1.04}^{x} = \frac{40}{20} = 2$

Hence $x = \frac{\log 2}{\log 1.04} = \frac{0.30103}{0.01703334} = 17.67$ years.