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A high school had 1200 students enrolled in 2003 and 1500 students in 2006. If the student population P: grows as a linear function of time t, where t is the number of years after 2003. Find a linear function that relates the student population to the time t.


A. P = 1200 t + 100
B. P = 100 t + 1000
C. P = 100 t + 1200
D. P = 1000 t + 100 ​

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Algebra Basics: What Are Polynomials? - Math Antics /9-6106I

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MYLENEMALINTADIN

Given: Population is a linear function of t.

⇒P=kt+C, where k and C are constants.

In 2003, given that P=1200,t=0

since t is time in years from 2003

⇒1200=k(0)+C

∴C=1200

In 2006 P=1500,t=2006−2003=3

⇒1500=k(3)+1200

∴k=100

(A) In 2010 t=2010−2003=7

P=100×7+1200=1900

(B) The linear function is P=100t+1200

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