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Chapter 12: Q 41. (page 825)
In Problems 39– 44, find each sum.
The sum of the given sequence is
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In Problems 61–70, express each sum using summation notation.
Roth IRA On January 1, 1999, Bob decided to place \(500 at the end of each quarter into a Roth Individual Retirement Account.
(a) Find a recursive formula that represents Bob’s balance at the end of each quarter if the rate of return is assumed to be 8% per annum compounded quarterly.
(b) How long will it be before the value of the account exceeds \)100,000?
(c) What will be the value of the account in 25 years when Bob retires?
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" ?
Growth of a Rabbit Colony:
A colony of rabbits begins with one pair of mature rabbits, which will produce a pair of offspring (one male, one female) each month. Assume that all rabbits mature in 1 month and produce a pair of offspring (one male, one female) after 2 months. If no rabbits ever die, how many pairs of mature rabbits are there after 7 months?
[Hint: The Fibonacci sequence models this colony. Do you see why?]
In Problems 17–28, write down the first five terms of each sequence.
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