A geologist is using stratigraphy to analyze the history of a canyon wall overlooking a river, in a region which used to be covered by a prehistoric ocean. She finds that in a certain location where there are few intrusions, the age of the rock layers can be (roughly) modeled as a function of the height above the canyon floor. She uses the function f(x) = 400e where a gives the height in feet and f (x) is the age in millions of years. -.05x +10 . Find dy as an approximation for Ay, for the interval [10, 20]. Then find Ay. • How good is this approximation? . What is the interpretation of Ay in context? Find dy for the interval [40, 50]. Then find Ay. How good is this approximation? O What is the interpretation of Ay in context? Compare the two estimates dy that you made for Ay, for the two intervals. What does the difference between these two estimates tell you in context? 50 million years old and wants to program her software
A geologist is using stratigraphy to analyze the history of a canyon wall overlooking a river, in a region which used to be covered by a prehistoric ocean. She finds that in a certain location where there are few intrusions, the age of the rock layers can be (roughly) modeled as a function of the height above the canyon floor. She uses the function f(x) = 400e where a gives the height in feet and f (x) is the age in millions of years. -.05x +10 . Find dy as an approximation for Ay, for the interval [10, 20]. Then find Ay. • How good is this approximation? . What is the interpretation of Ay in context? Find dy for the interval [40, 50]. Then find Ay. How good is this approximation? O What is the interpretation of Ay in context? Compare the two estimates dy that you made for Ay, for the two intervals. What does the difference between these two estimates tell you in context? 50 million years old and wants to program her software
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 geologist is using stratigraphy to analyze the history of a canyon wall overlooking a river, in a region which used to be
covered by a prehistoric ocean. She finds that in a certain location where there are few intrusions, the age of the rock layers
can be (roughly) modeled as a function of the height above the canyon floor. She uses the function f(x) = 400e-05 +10
where a gives the height in feet and f(x) is the age in millions of years.
• Find dy as an approximation for Ay, for the interval [10, 20]. Then find Ay.
How good is this approximation?
. What is the interpretation of Ay in context?
Find dy for the interval [40, 50]. Then find Ay.
. How good is this approximation?
. What is the interpretation of Ay in context?
Compare the two estimates dy that you made for Ay, for the two intervals. What does the difference between these two
estimates tell you in context?
Suppose she wants to estimate the height at which the rock layer 50 million years old, and wants to program her software
to use Newton's Method to do this approximation. What function could she use, that approximating a zero of that
function would give her this estimate?
What is a good seed value o for her to use?
Use the Newton's Method formula, and the seed value you chose, to estimate the height above the riverbed at which the
canyon wall rocks are 50 million years old.
Use technology to estimate the solution. What is the error on the c3 approximation?
12:15
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Transcribed Image Text:A geologist is using stratigraphy to analyze the history of a canyon wall overlooking a river, in a region which used to be
covered by a prehistoric ocean. She finds that in a certain location where there are few intrusions, the age of the rock layers
can be (roughly) modeled as a function of the height above the canyon floor. She uses the function f(x) = 400e-05 +10
where a gives the height in feet and f(x) is the age in millions of years.
• Find dy as an approximation for Ay, for the interval [10, 20]. Then find Ay.
How good is this approximation?
. What is the interpretation of Ay in context?
Find dy for the interval [40, 50]. Then find Ay.
. How good is this approximation?
. What is the interpretation of Ay in context?
Compare the two estimates dy that you made for Ay, for the two intervals. What does the difference between these two
estimates tell you in context?
Suppose she wants to estimate the height at which the rock layer 50 million years old, and wants to program her software
to use Newton's Method to do this approximation. What function could she use, that approximating a zero of that
function would give her this estimate?
What is a good seed value o for her to use?
Use the Newton's Method formula, and the seed value you chose, to estimate the height above the riverbed at which the
canyon wall rocks are 50 million years old.
Use technology to estimate the solution. What is the error on the c3 approximation?
12:15
Sign out
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