The exponential model A=58.7e^0.02t 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 89 million.

Answer:About 20.81 yearsStep-by-step explanation:89 million is the "final population" -- population after t years.So, 89 million would be in "A" in the equation. Then we will have to solve for "t" by taking LN (natural logarithm). That is how we solve exponential equations.So,[tex]A=58.7e^{0.02t}\\89=58.7e^{0.02t}\\\frac{89}{58.7}=e^{0.02t}\\1.5162=e^{0.02t}[/tex]Now we recognize the exponential rule of:Ln(e) = 1and we use the property:[tex]Ln(a^b)=bLn(a)[/tex]Now, we solve by taking Ln of both sides:[tex]1.5162=e^{0.02t}\\Ln(1.5162)=Ln(e^{0.02t})\\Ln(1.5162)=0.02tLn(e)\\Ln(1.5162)=0.02t\\t=\frac{Ln(1.5162)}{0.02}\\t=20.81[/tex]So, population would be 89 million in about 20.81 years