# 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 reach 240,000?

Feb 8, 2016

$99.713 \text{ }$years

#### Explanation:

Like in financial interest we have $P {\left(1 + \frac{1.4}{100}\right)}^{n}$

In this case it is :$\text{ } 60000 {\left(1 + \frac{1.4}{100}\right)}^{n} = 240000$

So$\text{ } {\left(1 + \frac{1.4}{100}\right)}^{n} = \frac{240}{60} = \frac{24}{6} = 4$

Taking logs

$n \ln \left(\frac{101.4}{100}\right) = \ln \left(4\right)$

$n = \ln \frac{4}{\ln \left(\frac{101.4}{100}\right)} \text{ "=" } \frac{\ln \left(4\right)}{\ln \left(101.4\right) - \ln \left(100\right)} = 99.713$
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$\textcolor{b l u e}{\text{Comment: }}$

This model does not allow for any deaths of the parents or caterpillars.