# In 2004, the population of butterflies in West Fremont is 60,000, and growing at a rate of 1.4% each year. If the rate of population growth remains constant, determine the year in which the population will double?

Apr 1, 2016

The population would have doubled in the year 2072

#### Explanation:

If the rate of growth is constrained as constant then this is the same as simple interest type calculation.

Let the number of years be $n$

$60000 + \left[\left(60000 \times \frac{1.4}{100}\right) \times n\right] = 60000 \times 2$

Subtract 60000 from both sides

$\implies \left(60000 \times \frac{1.4}{100}\right) \times n = 60000$

Divide both sides by $\left(60000 \times \frac{1.4}{100}\right)$

$\implies n = 60000 \times \frac{100}{60000 \times 1.4}$

$\implies n = \frac{100}{1.4} = 71.429$ years span to 3 decimal places

So the year in which this happens is

$2001 + 71 = 2072$