If an initial amount A, of money is invested at an interestrate r compounded n times a year, the value of the invest-ment after t years isA = A. 1 +If we let n → 0, we refer to the continuous compoundingof interest. Use l'Hospital's Rule to show that if interest iscompounded continuously, then the amount after t years isA = Age"

Given, The formula for amount A compounded n times is,…

Answered: If an initial amount A, of money is…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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If $P is invested for n years at 12% compounded continuously, the future value that results after n years is given by the function S = Pe0.12n. (a) At what rate is the future value growing at any time (for any nonnegative n)? Your answer cannot be understood or graded. More Information = (u),s (b) At what rate is the future value growing after 1 year (n = 1)? S'(1) = %3D
1.) Check off O all of the functions that show an exponential growth. O A.) y=2x+5 O B.) y=2* O C.) y=8(.9)* O D.) y=100 – 6x O E.) f(x)=12(1.016)* O F.) f(n)=24n² O G.) p(n)=23,000(1.05)"
The initial population size of rock ptarmigans in an area is 500 ptarmigans. The growth rate is 0.2 and the carrying capacity is 8000 ptarmigans. The authorities in the area have announced that it is possible to start hunting in the area when the size of the population has reached 5000 ptarmigans. Assume that time is measured in years. After how many years can a ptarmigan be allowed to hunt in the area if we assume that the population size is in accordance with the logistic equation? )?
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A client’s orders are growing consistently at x% per year. A) If three years from now orders are 50% higher than today, what is the annual growth rate (x)? B) Write an expression (in terms of x) for how many years it will take until orders are double what they are currently

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