(A) Find a simplified explicit form (in terms of s and t) for the amount of interest earned between times and time t, which is I = A(t) - A(s), where s < t, if a. In = n for some positive integer n. = a b. In = 2" for some positive integer n. Hint: The geometric sum of k terms is Σo ari = for a constant ratio r # 1. i=0 Total interest is the sum of the periodic interests, Is+1, Is+2,..., It. I₁ + + Is Is+1 It 0 A(s) S A(s+1) A(s+2) s+1 s +2 A(t-1) t-1 A(t) t
(A) Find a simplified explicit form (in terms of s and t) for the amount of interest earned between times and time t, which is I = A(t) - A(s), where s < t, if a. In = n for some positive integer n. = a b. In = 2" for some positive integer n. Hint: The geometric sum of k terms is Σo ari = for a constant ratio r # 1. i=0 Total interest is the sum of the periodic interests, Is+1, Is+2,..., It. I₁ + + Is Is+1 It 0 A(s) S A(s+1) A(s+2) s+1 s +2 A(t-1) t-1 A(t) t
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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Transcribed Image Text:(3) (A) Find a simplified explicit form (in terms of s and t) for the amount of interest earned between
times and time t, which is I = A(t) - A(s), where s < t, if
a. In = n for some positive integer n.
b. In = 2" for some positive integer n. Hint: The geometric sum of k terms is Σar² = a¹
1-rk+1
for a constant ratio r # 1.
Total interest is the sum of the periodic interests, Is+1, Is+2, … … .‚ It.
1₁ + + Is
Is+1 Is+2
It
0
A(s)
S
A(s+1) A(s+2)
s+1 s +2
A(t-1)
t-1
A(t)
t
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