The population of Sasquatch in Portage County is modeled by the function P(t) = 150t /t + 15 , where t = 0 represents the year 1803. When were there fewer than 140 Sasquatch in the county?

Question

I need to find the year

Answer 1

as written it says 150t/t + 15

which equals 150 + 15 = 165 forever, never changing or reaching 140.

but you probably meant 150t/(t+15),

then

set that equal to 140. 140 = 150t/(t+15)

14 = 15t(t+15)

14 = 15t^2 + 225t

15t^2 + 225t - 14 = 0

factor, complete the square or use the quadratic formula

probably no simple factors, so try one of the others.

divide by 15

t^2 + 9t = 14/15

t^2 + 9t + 81/4 = 14/15 + 81/4

(t+9/2)^2 = (56+1215)/60

t+9/2 = (1/2)sqr(1271/15)

t = -9/2 + or - (1/2)(9.2) = -4.5 + 4.6 = 0.1 (ignore the negative solution)

add 0.1 to 1803 to get

1803 plus one tenth of a year, or 1/10 times 12 months = 1.2 months = about 1 month + a week

maybe Feb. 7, 1803