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The breakdown of a sample of a chemical compound is represented by the
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28 Mar 2021, 22:50
28 Mar 2021, 22:50
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27% (01:02) correct
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The breakdown of a sample of a chemical compound is represented by the function \(c(n) = 200(0.5^n)\), where \(c(n)\) represents the number of milligrams of the substance that remains at the end of \(n\) years. Which of the following is true?
I. \(200\) represents the number of milligrams of the substance that remains after the first year
II. \(0.5\) represents the fraction of the starting amount by which the substance gets reduced by the end of each year
III. Each year the substance gets reduced by one-half of \(200\)
A. I only
B. II only
C. III only
D. I and III only
E. II and III only
I. \(200\) represents the number of milligrams of the substance that remains after the first year
II. \(0.5\) represents the fraction of the starting amount by which the substance gets reduced by the end of each year
III. Each year the substance gets reduced by one-half of \(200\)
A. I only
B. II only
C. III only
D. I and III only
E. II and III only
Re: The breakdown of a sample of a chemical compound is represented by the
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29 Mar 2021, 22:24
29 Mar 2021, 22:24
2
I. \(200\) represents the number of milligrams of the substance that remains after the first year
Plugin n=1, c = 100. False.
II. \(0.5\) represents the fraction of the starting amount by which the substance gets reduced by the end of each year
At the end of each year, c is multiplied by (0.5) when n increases for each year. Hence, the statement is true. If you recall the equation of compound interest, you would understand that this function of c(n) is similar to it.
III. Each year the substance gets reduced by one-half of \(200\)
Means each year, we subtract 100 from the value of c(n). This is not exactly what the function does. False.
IMO, B is the correct answer.
Plugin n=1, c = 100. False.
II. \(0.5\) represents the fraction of the starting amount by which the substance gets reduced by the end of each year
At the end of each year, c is multiplied by (0.5) when n increases for each year. Hence, the statement is true. If you recall the equation of compound interest, you would understand that this function of c(n) is similar to it.
III. Each year the substance gets reduced by one-half of \(200\)
Means each year, we subtract 100 from the value of c(n). This is not exactly what the function does. False.
IMO, B is the correct answer.
Re: The breakdown of a sample of a chemical compound is represented by the
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22 Dec 2024, 20:50
22 Dec 2024, 20:50
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