Answer:
2009
Step-by-step explanation:
The population P (in thousands) of Montana in the years 2005 through 2015 can be modeled by the equation:
[tex]P = 81 \ln(t) + 807, \quad 5 \leq t \leq 15[/tex]
where t represents the year, with t = 5 corresponding to 2005.
To determine the year in which the population of Montana exceeds 985 thousand, set 81 ln(t) + 807 greater than 985 and solve for t:
[tex]81 \ln(t) + 807 > 985 \\\\\\ 81 \ln (t) > 985-807\\\\\\ 81 \ln(t) > 178\\\\\\ \ln(t) > \dfrac{178}{81}\\\\\\e^{\ln(t)} > e^{\frac{178}{81}}\\\\\\t > e^{\frac{178}{81}}\\\\\\t > 9.0027570039...[/tex]
As t = 9.002757... corresponds with year 2009.002757..., this means that the population of Montana exceeds 985 thousand in the year 2009.
