t=0 corresponds to 2000 students enrolledt=15 corresponds to 9500 students enrolled The projected rate of increase in enrollment at Newhampton College is estimatedbydE5000(t + 1)-3/2,dt%3Dwhere E(t) is the projected enrollment in t years (t > 0). The leadership of Newhampton is beginning to draw up their 2025-2030 five-year plan.In order to estimate the expected revenue, they need to know how many students willbe added during those five years. What is the net change in students over that timeperiod? (Say that t = 0 corresponds to the current year, 2020)

Given, The projected rate of increase the enrollment student at Newhampton college is estimated by dEdt=5000(t+1)-32 (1) here t≥0 E(0)=2000 Since 2020 is the base year. in 2020 already enrolled student in Newhampton college 2000. By the separation of variable in equation (1), we have dE=5000(t+1)-32dt integrating with respect to t, we get E(t)=5000-2t+1+C (2) Here C is an arbitrary constant. Applying initial condition, we have E(0)=-100001+C⇒2000=-10000+C⇒C=12000 Hence equation (2) will be E(t)=-10000t+1+12000 The above equation is the enrolled students at time t years. Now in 5 years from 2020-2025, enrollment of students in the college is, E(5)=-100005+1+12000⇒E(5)=7918 Again in 10 years from 2020-2030, enrollment of students in the college is, E(10)=-1000010+1+12000⇒E(10)=8985 So the net change in the students in the time periods 2025-2030 is E(10)-E(5)=8985-7918=1067 Answer: The net change in the students in the time periods 2025-2030 is 1067.