The small town of Boringville had a population of 5200 in the year 2000. The birth and death rates of the people of Boringville are given by the following functions, where t is given in years after 2000: Birth rate: B(t) = t²e(t+¹)−¹ + 2 Death rate: D(t) = = t5 2t+1 a. What was the population of Boringville at the beginning of the year 2012? Round your answer to the nearest person. b. How many people were born in Boringville between the years 2000 and 2004? Round your answer to the nearest person. C. From the years 2000 to 2012, determine the minimum and maximum population of Boringville. d. At the start of 2007, is the population of Boringville increasing or decreasing?

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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The small town of Boringville had a population of 5200 in the year 2000. The birth and death rates of the people of Boringville are given by the following functions, where \( t \) is given in years after 2000:

\[ Birth\:rate: B(t) = t^2 e^{(t+1)^{-1}} + 2 \]

\[ Death\:rate: D(t) = \frac{t^5}{2^{t+1}} \]

a. What was the population of Boringville at the beginning of the year 2012? Round your answer to the nearest person.

b. How many people were born in Boringville between the years 2000 and 2004? Round your answer to the nearest person.

c. From the years 2000 to 2012, determine the minimum and maximum population of Boringville.

d. At the start of 2007, is the population of Boringville increasing or decreasing?
Transcribed Image Text:The small town of Boringville had a population of 5200 in the year 2000. The birth and death rates of the people of Boringville are given by the following functions, where \( t \) is given in years after 2000: \[ Birth\:rate: B(t) = t^2 e^{(t+1)^{-1}} + 2 \] \[ Death\:rate: D(t) = \frac{t^5}{2^{t+1}} \] a. What was the population of Boringville at the beginning of the year 2012? Round your answer to the nearest person. b. How many people were born in Boringville between the years 2000 and 2004? Round your answer to the nearest person. c. From the years 2000 to 2012, determine the minimum and maximum population of Boringville. d. At the start of 2007, is the population of Boringville increasing or decreasing?
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