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Published byQuentin Watkins Modified over 9 years ago
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Many times we are concerned with the “end behavior” of a function. That is, what does a function do as x approaches infinity. This becomes very important when something is a function of time, and we want to know the behavior as time extends into the future. Let’s look at our turkey population model from a previous assignment.
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The population of a flock of turkeys is modeled by the function: Let’s look at the graph of the function
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P, number of turkeys t, in years The population peaks around the 3 year mark and then seems to level off. By examining the limit as t approaches infinity, we can find the value where the population is leveling
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We wish to find: First, I will rewrite this as two limits:
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The first is a limit of constant so it equals 16. Let’s look at the second limit: This is much like 0/0, it is an indeterminate form so we have to “fix” it with algebra.
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The highest degree of t in the problem is 2, so let’s divide top and bottom by t 2 These terms go to 0 as t goes to infinity
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Since this limit is 0, the population is approaching the value of 16 as time increases.
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Here is an easier way to look at this. Since the degree of the denominator is greater than that of the numerator, it will dominate as t nears infinity. Dividing by a huge number will give a very small value, in fact, it will go to 0. 0
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