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The remaining amount, A (in grams), of a substance undergoing ra- dioactive decay is given by the function A = f(t,C), where C is the initial amount of the substance present (in grams) and t is the time that has passed, in years. Use the contour plot of f shown to the right to answer the following questions. 40 15 20 30 20 (a) How much of the substance must be present in the initial sample in order for there to be 15 grams remaining after 2 years? Include 10 units. 1 2 3 4 (b) Sketch a graph of the cross-section of f in which t = 2. Carefully label your axes, and then briefly explain what this graph tells you. (c) Sketch a graph of the cross-section of ƒ in which C = 40. Carefully label your axes, and then briefly explain what this graph tells you.

The remaining amount, A (in grams), of a substance undergoing ra- dioactive decay is given by the function A = f(t,C), where C is the initial amount of the substance present (in grams) and t is the time that has passed, in years. Use the contour plot of f shown to the right to answer the following questions. 40 15 20 30 20 (a) How much of the substance must be present in the initial sample in order for there to be 15 grams remaining after 2 years? Include 10 units. 1 2 3 4 (b) Sketch a graph of the cross-section of f in which t = 2. Carefully label your axes, and then briefly explain what this graph tells you. (c) Sketch a graph of the cross-section of ƒ in which C = 40. Carefully label your axes, and then briefly explain what this graph tells you.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 93E
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5. The remaining amount, A (in grams), of a substance undergoing ra- dioactive decay is given by the function A = f(t,C), where C is the initial amount of the substance present (in grams) and t is the time that has passed, in years. Use the contour plot of f shown to the right to answer the following questions. 40 15 20 10 30 20 (a) How much of the substance must be present in the initial sample in order for there to be 15 grams remaining after 2 years? Include 10 units. 1 2 3 4 6 (b) Sketch a graph of the cross-section of f in which t = 2. Carefully label your axes, and then briefly explain what this graph tells you. (c) Sketch a graph of the cross-section of f in which C = 40. Carefully label your axes, and then briefly explain what this graph tells you.
Transcribed Image Text:5. The remaining amount, A (in grams), of a substance undergoing ra- dioactive decay is given by the function A = f(t,C), where C is the initial amount of the substance present (in grams) and t is the time that has passed, in years. Use the contour plot of f shown to the right to answer the following questions. 40 15 20 10 30 20 (a) How much of the substance must be present in the initial sample in order for there to be 15 grams remaining after 2 years? Include 10 units. 1 2 3 4 6 (b) Sketch a graph of the cross-section of f in which t = 2. Carefully label your axes, and then briefly explain what this graph tells you. (c) Sketch a graph of the cross-section of f in which C = 40. Carefully label your axes, and then briefly explain what this graph tells you.
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