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The exponential model A = 178e^0007t describes the population, A, of a country in millions, t years after 2003. Use the model to determine when the population of the country will be 190 million.(Round to the nearest year as needed.)

Respuesta :

To determine how many years has passed we equate the population we need in the function and then we solve for t:

[tex]\begin{gathered} 190=178e^{0.007t} \\ e^{0.007t}=\frac{190}{178} \\ \ln e^{0.007t}=\ln (\frac{190}{178}) \\ 0.007t=\ln (\frac{190}{178}) \\ t=\frac{1}{0.007}\ln (\frac{190}{178}) \\ t=9.32 \end{gathered}[/tex]

This means that in nine years (approximately) the population will be 190 millions, therefore the population will be that amount in 2012.

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