Progressive High School had 1200 students enrolled in 2016 and 1500 students in 2019. If the student population P ; grows as a linear function of time t, where t is the number of years after 2015. How many students will be enrolled in the school in 2023?
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Answer:
1900 students will be enrolled in the school in 2023
Please look at the analysis
Let ' [tex]p=k(t-2015)+b[/tex] ' be the function.
When [tex]t=2016[/tex], [tex]P=1200[/tex]
So [tex]1200=k(2016-2015)+b[/tex]
⇒ [tex]1200=k+b[/tex] (1)
When [tex]t=2019[/tex], [tex]P=1500[/tex]
So [tex]1500=k(2019-2015)+b[/tex]
⇒ [tex]1500=4k+b[/tex] (2)
(2)-(1): [tex]1500-1200=4k+b-(k+b)[/tex]
⇒ [tex]300=3k[/tex]
⇒ [tex]k=100[/tex]
⇒ [tex]1200=k+b[/tex]
⇒ [tex]1200=100+b[/tex]
So [tex]b= 1100[/tex]
So the function is [tex]P=100(t-2015)+1100[/tex]
When [tex]t=2023[/tex],
⇒ [tex]P=100(2023-2015)+1100[/tex]
⇒ [tex]P=100[/tex] × [tex]8+1100[/tex]
⇒ [tex]P=1900[/tex]
So 1900 students will be enrolled in the school in 2023
(Application of function)
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