SOLUTION: In 2003, the owl population in a park was measured to be 340. By 2007, the population was measured again to be 285. The population changes linearly. a.Find a formula for the owl p

Algebra ->  Finance -> SOLUTION: In 2003, the owl population in a park was measured to be 340. By 2007, the population was measured again to be 285. The population changes linearly. a.Find a formula for the owl p      Log On


   

Question 1101441: In 2003, the owl population in a park was measured to be 340. By 2007, the population was measured again to be 285. The population changes linearly.
a.Find a formula for the owl population,P. Let the input be years since 2003.
b.What does your model predict the owl population to be in 2012?
show your work
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Plot time in yrs, +t+ on the horizontal
Plot population, +P+ on the vertical
Call the year 2003 +0+
--------------------------------
You are given the points:
( 0, 340 )
( 4, 285 )
Use the general point-slope formula
--------------------------------------
(a)
+%28+P+-+285+%29+%2F+%28+t+-+4+%29+=+%28+340+-+285+%29+%2F+%28+0+-+4+%29+
+%28+P+-+285+%29+%2F+%28+t+-+4+%29+=+55+%2F+%28-4%29+
+%28-4%29%2A%28+P+-+285+%29+=+55%2A%28+t+-+4+%29+
+-4P+%2B+1140+=+55t+-+220+
+-4P+=+55t+-+1360+
+P+=+%28-55%2F4%29%2At+%2B+340+
---------------------------
(b)
2012 = +9+
+P+=+%28-55%2F4%29%2A9+%2B+340+
+P+=+-495%2F4+%2B+340+
+P+=+-123.75+%2B+340+
+P+=+216.25+
In 2012 the population was 216 owls