Please help me! The population P (in thousands) of Alaska in the years 2005 through 2015 can be modeled by P = 75 ln(t) + 540, 5 ≤ t ≤ 15 where t represents the year, with t = 5 corresponding to 2005.

Question

Whole question:

The population P (in thousands) of Alaska in the years 2005 through 2015 can be modeled by P = 75 ln(t) + 540, 5 ≤ t ≤ 15 where t represents the year, with t = 5 corresponding to 2005. During which year did the population of Alaska exceed 730 thousand?

Answer 1

P = 75 ln(t) + 540

We are looking for t (the number of years after 2000) when P = 730 so:

730 = 75 ln(t) + 540 (subtract 540 from both sides to get:

190 = 75 ln(t) (divide both sides by 75 to get:

2.5333 = ln(t) which can be written as:

log_e( t ) = 2.5333 (converting the log expression to an exponential expression we get:

e^2.5333 = t

t = 12.595

The year is 2000 + t so the year is 2012

Answer 2

Hello Sydney!

You need to find the value of P > 730

Fromm the equation:

P = 75 ln(t) + 540

75 ln(t) + 540 = 730

75 ln(t) = 190

ln(t) = 2.53

t = 12.6

It was during 2012