-) Glacial Retreat. In 2014, Shakes Glacier had a length of 8530 feet but its terminus (the end of the glacier) was receding at a rate of 351 feet per year. Assume that the relationship between glacier length and time is linear. a) Determine a model for the Length, L, of Shakes Glacier as a function of time, t, in years. Let t =0 correspond to 2014. b) Use the model to determine the length of Shakes Glacier in 2020. c) Write, including units, and interpret the slope of the model.
-) Glacial Retreat. In 2014, Shakes Glacier had a length of 8530 feet but its terminus (the end of the glacier) was receding at a rate of 351 feet per year. Assume that the relationship between glacier length and time is linear. a) Determine a model for the Length, L, of Shakes Glacier as a function of time, t, in years. Let t =0 correspond to 2014. b) Use the model to determine the length of Shakes Glacier in 2020. c) Write, including units, and interpret the slope of the model.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:## Glacial Retreat
In 2014, Shakes Glacier had a length of 8530 feet, but its terminus (the end of the glacier) was receding at a rate of 351 feet per year. Assume that the relationship between glacier length and time is linear.
### Problem Set
a) **Determine a model** for the Length, \( L \), of Shakes Glacier as a function of time, \( t \), in years. Let \( t = 0 \) correspond to 2014.
b) **Use the model** to determine the length of Shakes Glacier in 2020.
c) **Write, including units, and interpret the slope** of the model.
d) **Write, as ordered pairs including units, and interpret the intercepts** of the model.
e) **Find the inverse** for your model.
f) **Verify your inverse** is correct using two appropriate compositions.
g) **Use the inverse function** to determine the year in which Shakes Glacier will be 5020 feet.
h) **Find the best contextual domain** for the problem that makes sense in the model’s context.
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