# The exponential growth model A=203e^(0.011t) describes the population of the United States, A, in millions, t years after 1970. When will the US population be 300 million?

Jul 10, 2016

22 January 2009.

#### Explanation:

Inversely,

$t = \frac{1}{0.01} \ln \left(\frac{A}{203}\right) = 100 \ln \left(\frac{A}{203}\right) y e a r s .$

So, when A = 300, $t = 100 \ln \left(\frac{300}{203}\right) = 39.0765$, years nearly,

since 1970.

The day on which this happens is ((0.0765)X365.25+1))th

day of 2009 and this is Jan 22, 2009.#