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Each year your salary is increased by $1,000 multiplied by the number of years you have com- pleted at the company. Thus, your salary for your first four years are t₁ = 100, 000, t₂ = 101,000, t3 = 103, 000, and t4 = 106, 000.

Each year your salary is increased by $1,000 multiplied by the number of years you have com- pleted at the company. Thus, your salary for your first four years are t₁ = 100, 000, t₂ = 101,000, t3 = 103, 000, and t4 = 106, 000.

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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plz provide answer of alll parts (i)(ii)(iii)(iv)(v)(vi) for part c

(i) Determine a recurrence relation for tn. + (ii) Identify whether t₁, t2, t3,... is an arithmetic sequence, geometric sequence, or quadratic sequence. (iii) Find an explicit formula for tn, clearly justifying why your formula is correct. (iv) Determine t15, your salary in the final year of your contract. (v) Determine a formula for the series Sn = t₁+t₂ +t3+...+ tn, which will be a function of n. Clearly show the steps in your calculation, and simplify your formula as much as possible. (vi) Determine S15, the cumulative amount you will have been paid after you complete your 15-year contract. Note: to answer item (v) above, apply one of the formulas you proved in Problem #2.
Transcribed Image Text:(i) Determine a recurrence relation for tn. + (ii) Identify whether t₁, t2, t3,... is an arithmetic sequence, geometric sequence, or quadratic sequence. (iii) Find an explicit formula for tn, clearly justifying why your formula is correct. (iv) Determine t15, your salary in the final year of your contract. (v) Determine a formula for the series Sn = t₁+t₂ +t3+...+ tn, which will be a function of n. Clearly show the steps in your calculation, and simplify your formula as much as possible. (vi) Determine S15, the cumulative amount you will have been paid after you complete your 15-year contract. Note: to answer item (v) above, apply one of the formulas you proved in Problem #2.
The job is such a perfect fit that you and your new CEO agree to a 15-year contract. You won't be making as much money as the recent contract signed by professional football player Patrick Mahomes (503 million dollars over 12 years), but thankfully your job description does not include being chased and tackled by 300-pound linemen! Let to be your annual salary in your nth year at the company, expressed in dollars. Your new boss offers you a starting salary of $100,000, with three different options for salary increases throughout your 15-year contract at this company. (a) Each year your salary is increased by $5,000. Thus, your salary for your first four years are t₁ = 100, 000, t2 = 105, 000, t3 = 110, 000, and t4 = 115,000. - (b) Each year your salary is increased by 4%. Thus, your salary for your first four years are t₁ = 100, 000, t2 = 104, 000, t3 = 108, 160, and t = 112, 486.40. (c) Each year your salary is increased by $1,000 multiplied by the number of years you have com- pleted at the company. Thus, your salary for your first four years are t₁ = 100, 000, t2 = 101, 000, t3 = 103, 000, and t4 106, 000.
Transcribed Image Text:The job is such a perfect fit that you and your new CEO agree to a 15-year contract. You won't be making as much money as the recent contract signed by professional football player Patrick Mahomes (503 million dollars over 12 years), but thankfully your job description does not include being chased and tackled by 300-pound linemen! Let to be your annual salary in your nth year at the company, expressed in dollars. Your new boss offers you a starting salary of $100,000, with three different options for salary increases throughout your 15-year contract at this company. (a) Each year your salary is increased by $5,000. Thus, your salary for your first four years are t₁ = 100, 000, t2 = 105, 000, t3 = 110, 000, and t4 = 115,000. - (b) Each year your salary is increased by 4%. Thus, your salary for your first four years are t₁ = 100, 000, t2 = 104, 000, t3 = 108, 160, and t = 112, 486.40. (c) Each year your salary is increased by $1,000 multiplied by the number of years you have com- pleted at the company. Thus, your salary for your first four years are t₁ = 100, 000, t2 = 101, 000, t3 = 103, 000, and t4 106, 000.
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