1. Let f(t) represent the amount of sea level rise, in mm, above mean sea level, where t represents time, in years, after the beginning of 2012. The table¹ below gives values for the function f. Estimate f'(3), and give units with your answer. Then, give a complete sentence explanation of your answer in the context of this problem. 3 t (years) 0 1 2 f(t) (mm) 56.2 67 67 72.5 4 82.3 2. The value of a car t years after it is purchased is given by V = f(t) dollars. (a) What are the units of f'(t)? Do you think that f'(t) is positive or negative? Explain, using a complete sentence. (b) Give complete sentence interpretations of the following two statements in the context of this problem: (i) f(1) = 27000 (ii) f'(1) = -1200 (c) Based on the information above, what do you predict the value of the car to be 2.5 years after it was purchased? Clearly show how you obtained your answer. 3. 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 t (minutes) 0 2 V (milliliters) H 8 10 0 20.3 38.4 48.7 55.1 59.3 (a) Estimate f'(6). Show your work, and include the correct units with your answer. (b) Give a complete sentence interpretation of f'(6) in the context of this problem. (c) Use your answer to part (a) to help you estimate the amount of hydrogen gas that has been produced 6.1 minutes after the start of the experiment. Please include the correct units with your answer.
1. Let f(t) represent the amount of sea level rise, in mm, above mean sea level, where t represents time, in years, after the beginning of 2012. The table¹ below gives values for the function f. Estimate f'(3), and give units with your answer. Then, give a complete sentence explanation of your answer in the context of this problem. 3 t (years) 0 1 2 f(t) (mm) 56.2 67 67 72.5 4 82.3 2. The value of a car t years after it is purchased is given by V = f(t) dollars. (a) What are the units of f'(t)? Do you think that f'(t) is positive or negative? Explain, using a complete sentence. (b) Give complete sentence interpretations of the following two statements in the context of this problem: (i) f(1) = 27000 (ii) f'(1) = -1200 (c) Based on the information above, what do you predict the value of the car to be 2.5 years after it was purchased? Clearly show how you obtained your answer. 3. 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 t (minutes) 0 2 V (milliliters) H 8 10 0 20.3 38.4 48.7 55.1 59.3 (a) Estimate f'(6). Show your work, and include the correct units with your answer. (b) Give a complete sentence interpretation of f'(6) in the context of this problem. (c) Use your answer to part (a) to help you estimate the amount of hydrogen gas that has been produced 6.1 minutes after the start of the experiment. Please include the correct units with your answer.
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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![**1.** Let \( f(t) \) represent the amount of sea level rise, in mm, above mean sea level, where \( t \) represents time, in years, after the beginning of 2012. The table below gives values for the function \( f \). Estimate \( f'(3) \), and give units with your answer. Then, give a complete sentence explanation of your answer in the context of this problem.
\[
\begin{array}{|c|c|}
\hline
t \, (\text{years}) & f(t) \, (\text{mm}) \\
\hline
0 & 56.2 \\
1 & 67 \\
2 & 67 \\
3 & 72.5 \\
4 & 82.3 \\
\hline
\end{array}
\]
**2.** The value of a car \( t \) years after it is purchased is given by \( V = f(t) \) dollars.
(a) What are the units of \( f'(t) \)? Do you think that \( f'(t) \) is positive or negative? Explain, using a complete sentence.
(b) Give complete sentence interpretations of the following two statements in the context of this problem:
- (i) \( f(1) = 27000 \)
- (ii) \( f'(1) = -1200 \)
(c) Based on the information above, what do you predict the value of the car to be 2.5 years after it was purchased? Clearly show how you obtained your answer.
**3.** 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.
\[
\begin{array}{|c|c|}
\hline
t \, (\text{minutes}) & V \, (\text{milliliters}) \\
\hline
0 & 0 \\
2 & 20.3 \\
4 & 38.4 \\
6 & 48.7 \\
8 & 55.1 \\
10 & 59.3 \\
\hline
\end{array}
\]
(a) Estimate \( f'(6) \). Show your work,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1bfda259-7429-4717-b69c-7067c249bba0%2Fa0545b58-2fa3-442e-b01b-f67cbed3b550%2Fvyglox7_processed.png&w=3840&q=75)
Transcribed Image Text:**1.** Let \( f(t) \) represent the amount of sea level rise, in mm, above mean sea level, where \( t \) represents time, in years, after the beginning of 2012. The table below gives values for the function \( f \). Estimate \( f'(3) \), and give units with your answer. Then, give a complete sentence explanation of your answer in the context of this problem.
\[
\begin{array}{|c|c|}
\hline
t \, (\text{years}) & f(t) \, (\text{mm}) \\
\hline
0 & 56.2 \\
1 & 67 \\
2 & 67 \\
3 & 72.5 \\
4 & 82.3 \\
\hline
\end{array}
\]
**2.** The value of a car \( t \) years after it is purchased is given by \( V = f(t) \) dollars.
(a) What are the units of \( f'(t) \)? Do you think that \( f'(t) \) is positive or negative? Explain, using a complete sentence.
(b) Give complete sentence interpretations of the following two statements in the context of this problem:
- (i) \( f(1) = 27000 \)
- (ii) \( f'(1) = -1200 \)
(c) Based on the information above, what do you predict the value of the car to be 2.5 years after it was purchased? Clearly show how you obtained your answer.
**3.** 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.
\[
\begin{array}{|c|c|}
\hline
t \, (\text{minutes}) & V \, (\text{milliliters}) \\
\hline
0 & 0 \\
2 & 20.3 \\
4 & 38.4 \\
6 & 48.7 \\
8 & 55.1 \\
10 & 59.3 \\
\hline
\end{array}
\]
(a) Estimate \( f'(6) \). Show your work,
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