The admission team at a new university are trying to predict the number of student applications they will receive each year. Let n be the number of years that the university has been open. The admissions team collect the following data for the first two years. Number of applications received in year n Year (n) 1 12300 2 12669 It is assumed that the number of students that apply to the university each year will follow a geometric sequence, un. In the first year there were 10380 places at the university available for applicants. The admissions team announce that the number of place available will increase by 600 every year. Let vn, represent the number of places available at the university in year n. For the first 10 years that the university is open, all places are filled. Students who receive a place each pay an $80 acceptance fee. When n = k, the number of places available will, for the first time, exceed the number of students applying. ate the percentage... MY for the her of student appo ******** c) Write down an expression for V₁. d) Calculate the total amount of acceptance fees paid to the university in the first 10 years. e) Find k f) State whether, for all n>k, the university will have places available for all applicants. Justify your answer.
The admission team at a new university are trying to predict the number of student applications they will receive each year. Let n be the number of years that the university has been open. The admissions team collect the following data for the first two years. Number of applications received in year n Year (n) 1 12300 2 12669 It is assumed that the number of students that apply to the university each year will follow a geometric sequence, un. In the first year there were 10380 places at the university available for applicants. The admissions team announce that the number of place available will increase by 600 every year. Let vn, represent the number of places available at the university in year n. For the first 10 years that the university is open, all places are filled. Students who receive a place each pay an $80 acceptance fee. When n = k, the number of places available will, for the first time, exceed the number of students applying. ate the percentage... MY for the her of student appo ******** c) Write down an expression for V₁. d) Calculate the total amount of acceptance fees paid to the university in the first 10 years. e) Find k f) State whether, for all n>k, the university will have places available for all applicants. Justify your answer.
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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Can someone please help with c-f? Thank you.
Transcribed Image Text:**Warm Up 10/17 – 10/21**
**Warm Up Monday (10/17)**
The admission team at a new university is attempting to predict the number of student applications they will receive each year. Let \( n \) be the number of years since the university has been established. The admissions team collected the following data for the first two years:
| Year (\( n \)) | Number of applications received in year \( n \) |
|----------------|-------------------------------------------------|
| 1 | 12300 |
| 2 | 12669 |
It is assumed that the number of students applying to the university each year will follow a geometric sequence, \( u_n \). In the first year, there were 10,380 places available for applicants at the university. The admissions team announced that the number of places available would increase by 600 each year. Let \( v_n \) represent the number of places available at the university in year \( n \). For the first 10 years that the university is open, all places are filled. Students who receive a place each pay an $80 acceptance fee. When \( n = k \), the number of places available will, for the first time, exceed the number of students applying.
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**Tasks:**
a) (Task details are obscured)
b) (Task details are obscured)
c) Write down an expression for \( v_n \).
d) Calculate the total amount of acceptance fees paid to the university in the first 10 years.
e) Find \( k \).
f) State whether, for all \( n \geq k \), the university will have places available for all applicants. Justify your answer.
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