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The number of students at a school increases at a rate proportional to its current size. In 2005, the school had 1700 students. In 2009, the school had 1850 students. Answer the following. 1) Write a differential equation that models this situation. Let P represent the student population and let t represent the number of years since 2005.

The number of students at a school increases at a rate proportional to its current size. In 2005, the school had 1700 students. In 2009, the school had 1850 students. Answer the following. 1) Write a differential equation that models this situation. Let P represent the student population and let t represent the number of years since 2005.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The number of students at a school increases at a rate proportional to its current size. In 2005, the school had 1700 students. In 2009, the school had 1850 students. Answer the following. 1) Write a differential equation that models this situation. Let P represent the student population and let t represent the number of years since 2005. 2) Solve for the general solution. 3) Solve for the particular solution in terms of P and t (find the values of all constants). 4) Determine what year the school's population will reach 2100. 5) Determine the rate at which the population is increasing in 2010. Include units in your answer.
Transcribed Image Text:The number of students at a school increases at a rate proportional to its current size. In 2005, the school had 1700 students. In 2009, the school had 1850 students. Answer the following. 1) Write a differential equation that models this situation. Let P represent the student population and let t represent the number of years since 2005. 2) Solve for the general solution. 3) Solve for the particular solution in terms of P and t (find the values of all constants). 4) Determine what year the school's population will reach 2100. 5) Determine the rate at which the population is increasing in 2010. Include units in your answer.
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