Answer:
- P(t) = 2200t +59,000
- 85,400 in 2012
Explanation:
You want a linear equation for the population P(t) for t = years since 2000, and the population in 2012, given it was 70,000 in 2005 and 76,600 in 2008.
Slope
The slope of the population function can be found using the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (76,600 -70,000)/(8 -5) = 6600/3 = 2200
Y-intercept
The y-intercept can be found using the equation ...
b = y -mx
b = 70,000 -2200(5) = 59,000
Equation
The equation for the population in slope-intercept form is ...
P(t) = mt +b
P(t) = 2200t +59000 . . . . equation for population
Year 2012
In 2012, t=12, so the population is ...
P(12) = 2200·12 +59000 = 85400
The population of the town in 2012 is 85400.
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