SOLUTION: The population of a town in 1920 was 2800 people. The town's population decreased linearly, and in 1926 the population was 2590. Find a formula for P, the town's population, in ter

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The population of a town in 1920 was 2800 people. The town's population decreased linearly, and in 1926 the population was 2590. Find a formula for P, the town's population, in ter      Log On


   

Question 807781: The population of a town in 1920 was 2800 people. The town's population decreased linearly, and in 1926 the population was 2590. Find a formula for P, the town's population, in terms of t, the number of years since 1920.
Found 2 solutions by josmiceli, josgarithmetic:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Use the general point-slope formula
+%28+2590+-+2800+%29+%2F+%28+6+-+0+%29+=+%28+P+-+2800+%29+%2F+%28+t+-+0+%29+
( note that 1926 is 6 yrs since 1920 )
+%28+2590+-+2800+%29+%2F+6+=+%28+P+-+2800+%29+%2F+t+
+%28+2590+-+2800+%29+%2F+6+=+%28+P+-+2800+%29+%2F+t+
+-210+%2F+6+=+%28+P+-+2800+%29+%2F+t+
+-210t+=+6%2A%28+P+-+2800+%29+
+-210t+=+6P+-+16800+
+6P+=+-210t+%2B+16800+
+P+=+-35t+%2B+2800+
--------------------
check:
+t+=+6+
+P+=+-35%2A6+%2B+2800+
+P+=+-210+%2B+2800+
+P+=+2590+
OK

Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Without first reaching for a more formal treatment, 6 years passed with loss of 2800-2590 people. This is 6 years for a decrease by 210 people, or 210/6=35 people lost per year.

A little more formally, P=-35%2At%2Bb, where b is the "P" intercept. YOU have one point for the line already, being (1920, 2800). Use this point to find b.
2800=-35%2A1920%2Bb
b=2800+35*1920
b=70000

Your model for this town's population is P=-35%2At%2B70000

This is not quite what you asked for, because that model did not account for "time since year 1920" but instead uses the actual year values, but maybe you could make the adjustment. Tell me if you have trouble with this.