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Chapter 12: Q 50. (page 825)
For Problems 45鈥�50, use a graphing utility to find the sum of each geometric sequence.
The sum of the given sequence is
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Environmental Control: The Environmental Protection Agency (EPA) determines that Maple Lake has 250 tons of pollutants as a result of industrial waste and that 10% of the pollutant present is neutralized by solar oxidation every year. The EPA imposes new pollution control laws that result in 15 tons of new pollutant entering the lake each year. The amount of pollutant in the lake at the end of each year is given by the recursively defined sequence
(a) Determine the amount of pollutant in the lake at the
end of the second year. That is, determine p2 .
(b) Using a graphing utility, provide pollutant amounts for
the next 20 years.
(c) What is the equilibrium level of pollution in Maple
Lake? That is, what is localid="1646823556776" ?
In Problems 61鈥�70, express each sum using summation notation.
In Problems 51鈥�66, determine whether each infinite geometric series converges or diverges. If it converges, find its sum.
In Problems 71-82, find the sum of each sequence.
A pond currently has 2000 trout in it. A fish hatchery decides to add an additional 20 trout each month. In addition, it is known that the trout population is growing 3% per month. The size of the population after n months is given by the recursively defined sequence.
(a) How many trout are in the pond at the end of the second month? That is, what is p2?
(b) Using a graphing utility, determine how long it will be
before the trout population reaches 5000.
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