Answered: Part A: Can I use a model to assist me…

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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Question

Olivia is researching the growth of sequoia trees and needs your assistance. She bought a Sequoia seedling from the gift shop at Sequoia National Park 20 years ago measuring 0.7 inches and planted it in her back yard. She is worried this tree is going to overtake her property because her nephew sprinkled magical exponential growth dust from Jack in Jack and the Bean Stalk. Review her research below to answer her questions.

Trees Growth Rates

*Growth Rate*	*Annual Height*
Fast	At least 2 feet
Medium	1 to 2 feet
Slow	At most 1 foot

The giant sequoia grows at a medium rate of an average of 18 inches per year to a height of 60 – 200 feet, a spread of 25 – 35 feet at maturity, and lives up to 3,000 years; however, Jack told my nephew the tree will now grow at a continual exponential rate of 17% each year.

Part A:
Can I use a model to assist me in predicting the height of my tree at different stages of its life? If so, create a model while explaining each step in the process and label each variable in context to her situation.

Part B:
How tall is my sequoia in 10 years? Explain your process so that she can replicate this to find the height of her tree after 50 years.

Part C:
A skyscraper is being built nearby with an overhang 150 feet directly above my property. Will the tree hit the skyscraper during my lifetime? Explain why or why not.

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