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Tori is draining her pool for winter. After the pool had started draining, Tori began to wonder how long it would take, and so they took some measurements. Four hours after opening the drain, the water was 5.5 feet deep. Seven hours after opening the drain, the water was 3 feet deep. For simplicity, Tori assumes that the depth of the water, d(t), can be modeled as a linear function of the time t, in hours, that the pool has been draining. a. Find this model, d(t), that gives the depth of the pool in feet t hours after the drain is opened. Show all work algebraically. b. Find the slope of your model, d(t), and interpret the slope in context. Fully explain your answer. C. Find the d-intercept for your model and interpret this value in context. Show all work algebraically.

Tori is draining her pool for winter. After the pool had started draining, Tori began to wonder how long it would take, and so they took some measurements. Four hours after opening the drain, the water was 5.5 feet deep. Seven hours after opening the drain, the water was 3 feet deep. For simplicity, Tori assumes that the depth of the water, d(t), can be modeled as a linear function of the time t, in hours, that the pool has been draining. a. Find this model, d(t), that gives the depth of the pool in feet t hours after the drain is opened. Show all work algebraically. b. Find the slope of your model, d(t), and interpret the slope in context. Fully explain your answer. C. Find the d-intercept for your model and interpret this value in context. Show all work algebraically.

Calculus: Early Transcendentals
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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Tori is draining her pool for winter. After the pool had started draining, Tori began to wonder how long it would take, and so they took some measurements. Four hours after opening the drain, the water was 5.5 feet deep. Seven hours after opening the drain, the water was 3 feet deep. For simplicity, Tori assumes that the depth of the water, d(t), can be modeled as a linear function of the time t, in hours, that the pool has been draining. а. Find this model, d(t), that gives the depth of the pool in feet t hours after the drain is opened. Show all work algebraically. b. Find the slope of your model, d (t), and interpret the slope in context. Fully explain your answer. С. Find the d-intercept for your model and interpret this value in context. Show all work algebraically. d. Find the t-intercept for your model and interpret this value in context. Show all work algebraically. Use your model to find d(2) and interpret this value in context. Show all work е. algebraically. Write the equation for d-(y). Show all work algebraically. g. Use your model to solve d(t) = 4 for t and interpret this value in context. Show all work f. algebraically. h. What is a reasonable domain and range for d(t)? Justify your answer fully.
Transcribed Image Text:Tori is draining her pool for winter. After the pool had started draining, Tori began to wonder how long it would take, and so they took some measurements. Four hours after opening the drain, the water was 5.5 feet deep. Seven hours after opening the drain, the water was 3 feet deep. For simplicity, Tori assumes that the depth of the water, d(t), can be modeled as a linear function of the time t, in hours, that the pool has been draining. а. Find this model, d(t), that gives the depth of the pool in feet t hours after the drain is opened. Show all work algebraically. b. Find the slope of your model, d (t), and interpret the slope in context. Fully explain your answer. С. Find the d-intercept for your model and interpret this value in context. Show all work algebraically. d. Find the t-intercept for your model and interpret this value in context. Show all work algebraically. Use your model to find d(2) and interpret this value in context. Show all work е. algebraically. Write the equation for d-(y). Show all work algebraically. g. Use your model to solve d(t) = 4 for t and interpret this value in context. Show all work f. algebraically. h. What is a reasonable domain and range for d(t)? Justify your answer fully.
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