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• What indeterminate form does nt lim,00 (1+)" have? • Let L = nt lim,-+0 (1+ )", and take the natural logarithm of both sides of this equation. Why can we change In (lim, (1+)) to In(1 limn→0

• What indeterminate form does nt lim,00 (1+)" have? • Let L = nt lim,-+0 (1+ )", and take the natural logarithm of both sides of this equation. Why can we change In (lim, (1+)) to In(1 limn→0

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter6: Exponential And Logarithmic Functions
Section6.1: Exponential Functions
Problem 68SE: An investment account with an annual interest rateof 7 was opened with an initial deposit of 4,000...
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A savings account with an interest rate r, which is compounded n times per year, and begins with P as the principal (initial amount), has the discrete nt compounding formula A (t) = P(1+ )". This is because we multiply the amount by itself plus a small amount, determined by the interest rate, and the account grows each time the compounding occurs. For continuous compounding, we use the formula A (t) Pert, and if we have seen this formula before, we may not have gotten a satisfactory answer as to why we use it, other than some vague notion of "compounding infinity times per year". In this exercise, we'll use Bernoulli's Rule to find the connection. It might be helpful to review the "Indeterminate Powers" section of the video before beginning.
Transcribed Image Text:A savings account with an interest rate r, which is compounded n times per year, and begins with P as the principal (initial amount), has the discrete nt compounding formula A (t) = P(1+ )". This is because we multiply the amount by itself plus a small amount, determined by the interest rate, and the account grows each time the compounding occurs. For continuous compounding, we use the formula A (t) Pert, and if we have seen this formula before, we may not have gotten a satisfactory answer as to why we use it, other than some vague notion of "compounding infinity times per year". In this exercise, we'll use Bernoulli's Rule to find the connection. It might be helpful to review the "Indeterminate Powers" section of the video before beginning.
• What indeterminate form does nt lim,0 (1+)" have? • Let L = lim,n→∞ (1+ -)", and take the natural n nt logarithm of both sides of this equation. Why can we change In (lim, - (1 + ;)") to lim, 4∞ In ( (1+ )): r
Transcribed Image Text:• What indeterminate form does nt lim,0 (1+)" have? • Let L = lim,n→∞ (1+ -)", and take the natural n nt logarithm of both sides of this equation. Why can we change In (lim, - (1 + ;)") to lim, 4∞ In ( (1+ )): r
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