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will be infected in 45 days? 4. Suppose bacteria in a population divide in 2 every hour and 90% of the current population dies after reproduction, not including the new offspring. If the population initially has 10 million bacteria, predict how many there will be in 12 hours. 5. In a rabbit population, each pair produces 12 offenning cted, how many individuals

will be infected in 45 days? 4. Suppose bacteria in a population divide in 2 every hour and 90% of the current population dies after reproduction, not including the new offspring. If the population initially has 10 million bacteria, predict how many there will be in 12 hours. 5. In a rabbit population, each pair produces 12 offenning cted, how many individuals

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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my attays to the costa ¹ = 1: N(t) remains constant As we see, there are only two options for solution of linear difference equations: ever-faster growth or decay to zero or another constant value. The exponential growth of populations is also known as Malthusian after the early population modeler Thomas Malthus. He used a simple population model with constant growth rate to predict demographic disaster due to the exponentially increasing population outstripping the growth in food production. In fact, human population has not been growing with a constant birth rate, and food production has only as good as the assumptions that underlie them. (so far) kept up pace with population size, illustrating yet again that mathematical models are 10.2.4 Exercises V For the following scenarios for a population: 1) Construct a dynamic model by writing down a difference equation both in the updating function form (N(t+1) = f(N(t))) and the increment form (N(t+1) - N(t) = g(N(t))) and specify the time step; 2) find the solution of the linear difference equation with a generic initial value and check that it satisfies the difference equation and predict the future. by plugging the solution into your equation (in either form); 3) plug in the given initial value 1. Zombies have appeared in Chicago. Every day, each zombie produces 3 new zombies. days? Suppose that initially there is only one zombie, how many zombies will there be in 7 2. Suppose hunters kill 50 deer in a national forest every hunting season, while the deer by predict how many there will be in 5 themselves have equal birth and death rates. If there are initially 500 deer in the forest, years. 3. The number of infected people in a population grows by 8% per day and those who will be infected in 45 days? become infected remain infected. If initially there are 8 infected, how many individuals 4. Suppose bacteria in a population divide in 2 every hour and 90% of the current population dies after reproduction, not including the new offspring. If the population initially has 10 million bacteria, predict how many there will be in 12 hours. 5. In a rabbit population, each pair produces 1.2 offspring every year (i.e. 0.6 per capita) and the adults have a 0.5 annual death rate after reproduction (and assume the whole many there will be in 5 years. population is paired up into mating pairs.) If initially there are 100 rabbits, predict how 6. Consider the same rabbit population, but now a python that lives nearby eats exactly 1 years? rabbit a month. If initially there are 100 rabbits, how many do you predict will be in 10 162 16
Transcribed Image Text:my attays to the costa ¹ = 1: N(t) remains constant As we see, there are only two options for solution of linear difference equations: ever-faster growth or decay to zero or another constant value. The exponential growth of populations is also known as Malthusian after the early population modeler Thomas Malthus. He used a simple population model with constant growth rate to predict demographic disaster due to the exponentially increasing population outstripping the growth in food production. In fact, human population has not been growing with a constant birth rate, and food production has only as good as the assumptions that underlie them. (so far) kept up pace with population size, illustrating yet again that mathematical models are 10.2.4 Exercises V For the following scenarios for a population: 1) Construct a dynamic model by writing down a difference equation both in the updating function form (N(t+1) = f(N(t))) and the increment form (N(t+1) - N(t) = g(N(t))) and specify the time step; 2) find the solution of the linear difference equation with a generic initial value and check that it satisfies the difference equation and predict the future. by plugging the solution into your equation (in either form); 3) plug in the given initial value 1. Zombies have appeared in Chicago. Every day, each zombie produces 3 new zombies. days? Suppose that initially there is only one zombie, how many zombies will there be in 7 2. Suppose hunters kill 50 deer in a national forest every hunting season, while the deer by predict how many there will be in 5 themselves have equal birth and death rates. If there are initially 500 deer in the forest, years. 3. The number of infected people in a population grows by 8% per day and those who will be infected in 45 days? become infected remain infected. If initially there are 8 infected, how many individuals 4. Suppose bacteria in a population divide in 2 every hour and 90% of the current population dies after reproduction, not including the new offspring. If the population initially has 10 million bacteria, predict how many there will be in 12 hours. 5. In a rabbit population, each pair produces 1.2 offspring every year (i.e. 0.6 per capita) and the adults have a 0.5 annual death rate after reproduction (and assume the whole many there will be in 5 years. population is paired up into mating pairs.) If initially there are 100 rabbits, predict how 6. Consider the same rabbit population, but now a python that lives nearby eats exactly 1 years? rabbit a month. If initially there are 100 rabbits, how many do you predict will be in 10 162 16
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