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) Find the value(s) of the constant k such that the following sum holds +00 Σ4· (k)2 = 9. i=2 You are allowed to use your graphical calculator to find zeroes of a function.

) Find the value(s) of the constant k such that the following sum holds +00 Σ4· (k)2 = 9. i=2 You are allowed to use your graphical calculator to find zeroes of a function.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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a) Find the value(s) of the constant k such that the following sum holds +∞o Σ4. (k)2 = 9. i=2 You are allowed to use your graphical calculator to find zeroes of a function. b) Homer runs a tree nursery growing apple trees. At the beginning of the year 2020 he had 2000 apple trees. In the course of a year, 5% of the trees die off and must be removed. Of the remaining trees, he sells 20% to clients every year in December (the right time for replanting). At the end of each year, Homer plants 300 new apple trees. i. Write down a recursive equation with initial condition for the number of apple trees a, in Homer's tree nursery at the start of the year 2020+ n. Use the general term of the sequence a, to find the number of apple trees in Homer's nursery at the beginning of the year 2027. How many apple trees will Homer have in the long run? Homer decides to retire and leaves his tree nursery to his granddaughter Maggie. She installs a new sprinkler system that reduces the percentage of apple trees dying in the course of a year to 3.5%, while still planting 300 new trees at the end of each year. Moreover, Maggie wants to evolve towards 1200 apple trees in the long run. Which percentage of the trees should she sell each year in December to make this happen? (Round your answer to two decimals.) ii. iii. iv.
Transcribed Image Text:a) Find the value(s) of the constant k such that the following sum holds +∞o Σ4. (k)2 = 9. i=2 You are allowed to use your graphical calculator to find zeroes of a function. b) Homer runs a tree nursery growing apple trees. At the beginning of the year 2020 he had 2000 apple trees. In the course of a year, 5% of the trees die off and must be removed. Of the remaining trees, he sells 20% to clients every year in December (the right time for replanting). At the end of each year, Homer plants 300 new apple trees. i. Write down a recursive equation with initial condition for the number of apple trees a, in Homer's tree nursery at the start of the year 2020+ n. Use the general term of the sequence a, to find the number of apple trees in Homer's nursery at the beginning of the year 2027. How many apple trees will Homer have in the long run? Homer decides to retire and leaves his tree nursery to his granddaughter Maggie. She installs a new sprinkler system that reduces the percentage of apple trees dying in the course of a year to 3.5%, while still planting 300 new trees at the end of each year. Moreover, Maggie wants to evolve towards 1200 apple trees in the long run. Which percentage of the trees should she sell each year in December to make this happen? (Round your answer to two decimals.) ii. iii. iv.
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