Question

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.)

Answer 1

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

`\begin{gathered} 190=178e^(0.007t) \\ e^(0.007t)=(190)/(178) \\ \ln e^(0.007t)=\ln ((190)/(178)) \\ 0.007t=\ln ((190)/(178)) \\ t=(1)/(0.007)\ln ((190)/(178)) \\ t=9.32 \end{gathered}`

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