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1. During a laboratory experiment, hydrochloric acid reacts with zinc to produce hydrogen gas. The table below shows the total volume, V = f(t), of hydrogen gas that has been produced t minutes after the start of the experiment. t (minutes) 0 2 V (milliliters) 0 H 4 6 8 10 20.3 38.4 48.7 55.1 59.3 (a) Find f(4), and include the correct units with your answer. (b) Estimate f'(4). Show your work, and include the correct units with your answer. (c) Give a complete sentence interpretation of f'(4) in the context of this problem.

1. During a laboratory experiment, hydrochloric acid reacts with zinc to produce hydrogen gas. The table below shows the total volume, V = f(t), of hydrogen gas that has been produced t minutes after the start of the experiment. t (minutes) 0 2 V (milliliters) 0 H 4 6 8 10 20.3 38.4 48.7 55.1 59.3 (a) Find f(4), and include the correct units with your answer. (b) Estimate f'(4). Show your work, and include the correct units with your answer. (c) Give a complete sentence interpretation of f'(4) in the context of this problem.

Advanced Engineering Mathematics
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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Homework 4 Math 161-001 Note: Please do these problems on your own paper, and not on this assignment sheet, so that there's plenty of space to write legibly and show your work. Then upload a pdf file of your work to Canvas. 1. During a laboratory experiment, hydrochloric acid reacts with zinc to produce hydrogen gas. The table below shows the total volume, V = f(t), of hydrogen gas that has been produced t minutes after the start of the experiment. 4 6 8 10 t (minutes) 0 2 V (milliliters) 0 20.3 38.4 48.7 55.1 59.3 (a) Find f(4), and include the correct units with your answer. (b) Estimate f'(4). Show your work, and include the correct units with your answer. (c) Give a complete sentence interpretation of f'(4) in the context of this problem. f(x) 2. To the right, you are given the graph of a function f. List the following quantities in order from smallest to largest. 0, f'(0.4), f'(1), f'(1.8), ƒ'(3), f'(3.6) Then, explain, using a complete sentence (or sentences), the strategy you used to rank the quantities. 3. To the right, you are given the graph of the function P = f(t) = 100 1.5t, which gives the population of a bacteria colony, P, after t hours. (a) Use the graph to estimate f'(1), and give a complete sen- tence interpretation of your answer in the context of this problem. (b) Use the limit definition of the derivative and a table to approximate f'(1) to within 0.1 of its true value. Show your table, and circle your final answer. 1 P 600 500 400 300 200 100 2 f(t) = 100-1.5t 1 2 3 4 4 X t
Transcribed Image Text:Homework 4 Math 161-001 Note: Please do these problems on your own paper, and not on this assignment sheet, so that there's plenty of space to write legibly and show your work. Then upload a pdf file of your work to Canvas. 1. During a laboratory experiment, hydrochloric acid reacts with zinc to produce hydrogen gas. The table below shows the total volume, V = f(t), of hydrogen gas that has been produced t minutes after the start of the experiment. 4 6 8 10 t (minutes) 0 2 V (milliliters) 0 20.3 38.4 48.7 55.1 59.3 (a) Find f(4), and include the correct units with your answer. (b) Estimate f'(4). Show your work, and include the correct units with your answer. (c) Give a complete sentence interpretation of f'(4) in the context of this problem. f(x) 2. To the right, you are given the graph of a function f. List the following quantities in order from smallest to largest. 0, f'(0.4), f'(1), f'(1.8), ƒ'(3), f'(3.6) Then, explain, using a complete sentence (or sentences), the strategy you used to rank the quantities. 3. To the right, you are given the graph of the function P = f(t) = 100 1.5t, which gives the population of a bacteria colony, P, after t hours. (a) Use the graph to estimate f'(1), and give a complete sen- tence interpretation of your answer in the context of this problem. (b) Use the limit definition of the derivative and a table to approximate f'(1) to within 0.1 of its true value. Show your table, and circle your final answer. 1 P 600 500 400 300 200 100 2 f(t) = 100-1.5t 1 2 3 4 4 X t
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