Question

The population of a small town in central Florida has shown a linear decline in the years 1992-2000. In 1992 the population was 48000 people. In 2000 it was 44880 people.

A) Write a linear equation expressing the population of the town P
P
in terms of t
t
, the number of years since 1992.
Answer: c

B) If the town is still experiencing a linear decline, what will the population be in 2003?

Answer 1

• P = -390t +48,000
• P = 43,710 in 2003

Explanation:

A) We are given two pairs of (t, P): (0, 48000), (8, 44880). We can use these with the 2-point form of the equation of a line:

y = (y2 -y1)/(x2 -x1)(x -x1) +y1

P = (44880 -48000)/(8 -0)(t -0) +48000

P = -3120/8t +48000

P = -390t +48000

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B) In 2003, t = 11, so we have ...

P = -390(11) +48000 = 43710

The population in 2003 is predicted to be 43,710.