From 2025 to 2030 there is a net change of 1067 students.(t=0 corresponding to the current year, 2020) About 1/3 of Newhampton's students live on-campus, while the other 2/3 live off-campus. The campus leadership estimates that the college earns $10,000 in tuitionand fees for every off-campus student and $15, 000 in tuition and fees per on-campusstudent. Using your answer from the previous question, project the net change in revenuefrom tuition and fees over the 2025-2030 time period. 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).

Isolate the variables E and t in the given differential equation. dEdt=5000t+1-32dE=5000t+1-32dt

Answered: |The projected rate of increase in…

|The projected rate of increase in enrollment at Newhampton College is estimated |by dE 5000(t + 1)~3/2, dt where E(t) is the projected enrollment in t years (t > 0).

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter7: Systems Of Equations And Inequalities

Section7.1: Systems Of Linear Equations: Two Variables

Problem 2SE: If you are performing a break-even analysis for a business and their cost and revenue equations are...

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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

From 2025 to 2030 there is a net change of 1067 students.

(t=0 corresponding to the current year, 2020)

About 1/3 of Newhampton's students live on-campus, while the other 2/3 live off-
campus. The campus leadership estimates that the college earns $10,000 in tuition
and fees for every off-campus student and $15, 000 in tuition and fees per on-campus
student. Using your answer from the previous question, project the net change in revenue
from tuition and fees over the 2025-2030 time period.

The projected rate of increase in enrollment at Newhampton College is estimated
by
dE
5000(t + 1)-3/2,
dt
%3D
where E(t) is the projected enrollment in t years (t > 0).

Expert Solution

Step 1

Isolate the variables E and t in the given differential equation.

$\begin{array}{rcl} \frac{d E}{d t} & = & 5000 {(t + 1)}^{- \frac{3}{2}} \\ d E & = & 5000 {(t + 1)}^{- \frac{3}{2}} d t \end{array}$

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