(a) In each of the following problems, you may assume that an exponential growth and decay model applies. i. A radioactive sample, with an initial mass of 200g, will decay to 140g in 10 years. Find the half-life of the sample. ii. The population of a rat colony is now 1,000 individuals, and is currently growing at a rate of 80 rats per year. Find a formula for the number of rats after t years. iii. An investment of $2,000 is invested at a nominal rate of 8% interest, compounded continuously. A. Find the value of the investment in 50 years. B. Find the effective annual rate (APR).
(a) In each of the following problems, you may assume that an exponential growth and decay model applies. i. A radioactive sample, with an initial mass of 200g, will decay to 140g in 10 years. Find the half-life of the sample. ii. The population of a rat colony is now 1,000 individuals, and is currently growing at a rate of 80 rats per year. Find a formula for the number of rats after t years. iii. An investment of $2,000 is invested at a nominal rate of 8% interest, compounded continuously. A. Find the value of the investment in 50 years. B. Find the effective annual rate (APR).
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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Solve 2(a) for at least iii or i.These question focus on exponential growth and decay.
Transcribed Image Text:i.
6x n (3x²+5) dx
3π/2
ii. ³7/² cos(x + π) dæ
2. Exponential Growth & Decay
iii. fx²√x + 1 dx
iv. ella dx
fo
(a) In each of the following problems, you may assume that an exponential growth and decay
model applies.
i. A radioactive sample, with an initial mass of 200g, will decay to 140g in 10 years.
Find the half-life of the sample.
ii. The population of a rat colony is now 1,000 individuals, and is currently growing
at a rate of 80 rats per year. Find a formula for the number of rats after t years.
iii. An investment of $2,000 is invested at a nominal rate of 8% interest, compounded
continuously.
A. Find the value of the investment in 50 years.
B. Find the effective annual rate (APR).
3. Integration by Parts
Write the integration by parts formula and explain the notation used.
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