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Initially, a forest is home to a population of 1,000 bunnies, but, due to environmental factors, the size of the population changes over time. The graphs of the birthrate, B(t), and death rate, D(t), for the population are shown below (here t is measured in years). y = D(t) y = B(t) t 10 15 20 25 30 35 40 (a) In one or two sentences, write down an interpretation of the definite integral 10 | (B(t) – D(t)) dt in the context of this problem. (b) Will the population after 10 years be greater or less than the initial population? Write one or two sentences explaining your answer. (c) Is there a time t > 0 at which the population will again be the same size as the initial population? If so, provide a rough estimate of this time, and write one or two sentences explaining how you found it. (d) Suppose you know that the average birth rate over the first 40 years is 100 bunnies/year and the average death rate over the first 40 years is 110 bunnies/year. How many bunnies are there in the population at t = 40? Show your work.

Initially, a forest is home to a population of 1,000 bunnies, but, due to environmental factors, the size of the population changes over time. The graphs of the birthrate, B(t), and death rate, D(t), for the population are shown below (here t is measured in years). y = D(t) y = B(t) t 10 15 20 25 30 35 40 (a) In one or two sentences, write down an interpretation of the definite integral 10 | (B(t) – D(t)) dt in the context of this problem. (b) Will the population after 10 years be greater or less than the initial population? Write one or two sentences explaining your answer. (c) Is there a time t > 0 at which the population will again be the same size as the initial population? If so, provide a rough estimate of this time, and write one or two sentences explaining how you found it. (d) Suppose you know that the average birth rate over the first 40 years is 100 bunnies/year and the average death rate over the first 40 years is 110 bunnies/year. How many bunnies are there in the population at t = 40? Show your work.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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Initially, a forest is home to a population of 1,000 bunnies, but, due to environmental factors, the size of the population changes over time. The graphs of the birthrate, B(t), and death rate, D(t), for the population are shown below (here t is measured in years). y = D(t) y = B(t) t 10 15 20 25 30 35 40 (a) In one or two sentences, write down an interpretation of the definite integral 10 | (B(t) – D(t)) dt - 0, in the context of this problem. (b) Will the population after 10 years be greater or less than the initial population? Write one or two sentences explaining your answer. (c) Is there a time t > 0 at which the population will again be the same size as the initial population? If so, provide a rough estimate of this time, and write one or two sentences explaining how you found it. (d) Suppose you know that the average birth rate over the first 40 years is 100 bunnies/year and the average death rate over the first 40 years is 110 bunnies/year. How many bunnies are there in the population at t = 40? Show your work.
Transcribed Image Text:Initially, a forest is home to a population of 1,000 bunnies, but, due to environmental factors, the size of the population changes over time. The graphs of the birthrate, B(t), and death rate, D(t), for the population are shown below (here t is measured in years). y = D(t) y = B(t) t 10 15 20 25 30 35 40 (a) In one or two sentences, write down an interpretation of the definite integral 10 | (B(t) – D(t)) dt - 0, in the context of this problem. (b) Will the population after 10 years be greater or less than the initial population? Write one or two sentences explaining your answer. (c) Is there a time t > 0 at which the population will again be the same size as the initial population? If so, provide a rough estimate of this time, and write one or two sentences explaining how you found it. (d) Suppose you know that the average birth rate over the first 40 years is 100 bunnies/year and the average death rate over the first 40 years is 110 bunnies/year. How many bunnies are there in the population at t = 40? Show your work.
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