The population P (in thousands) of Montana in the years 2005 through 2015 can be modeled by
P = 81 ln(t) + 807, 5 ≤ t ≤ 15
where t represents the year, with
t = 5
corresponding to 2005.† During which year did the population of Montana exceed 985 thousand?

Question

28-04-2024
Mathematics

Answered

The population P (in thousands) of Montana in the years 2005 through 2015 can be modeled by
P = 81 ln(t) + 807, 5 ≤ t ≤ 15
where t represents the year, with
t = 5
corresponding to 2005.† During which year did the population of Montana exceed 985 thousand?

Answer :

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semsee45 semsee45 · Answer 1 · 2024-04-28T04:42:40-04:00

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.

The population P (in thousands) of Montana in the years 2005 through 2015 can be modeled by P = 81 ln(t) + 807, 5 ≤ t ≤ 15 where t represents the year, with t = 5 corresponding to 2005.† During which year did the population of Montana exceed 985 thousand?

Answer :

Other Questions

The population P (in thousands) of Montana in the years 2005 through 2015 can be modeled by
P = 81 ln(t) + 807, 5 ≤ t ≤ 15
where t represents the year, with
t = 5
corresponding to 2005.† During which year did the population of Montana exceed 985 thousand?