Asked by gaconnectionsansw3r
For questions 1 and 2, graph the function.
y = 5one-half to the x power+ 4
(1 point)
Responses
Graph AThe function passes through the points left-parenthesis 1 comma negative 6.5 right-parenthesis, left-parenthesis 2 comma negative 5.25 right-parenthesis, and left-parenthesis 3 comma negative 4.625 right-parenthesis. As x approaches infinity, y approaches negative 4.
Image with alt text: Graph A The function passes through the points left-parenthesis 1 comma negative 6.5 right-parenthesis, left-parenthesis 2 comma negative 5.25 right-parenthesis, and left-parenthesis 3 comma negative 4.625 right-parenthesis. As x approaches infinity, y approaches negative 4.
Graph BAs x approaches negative infinity, y approaches 4. The function passes through the points left-parenthesis negative 1 comma 1.5 right-parenthesis, left-parenthesis 0 comma negative 1 right-parenthesis, and left-parenthesis 1 comma negative 6 right-parenthesis
Image with alt text: Graph B As x approaches negative infinity, y approaches 4. The function passes through the points left-parenthesis negative 1 comma 1.5 right-parenthesis, left-parenthesis 0 comma negative 1 right-parenthesis, and left-parenthesis 1 comma negative 6 right-parenthesis
Graph CThe function passes through the points left-parenthesis 1 comma 6.5 right-parenthesis, left-parenthesis 2 comma 5.25 right-parenthesis, and left-parenthesis 3 comma 4.625 right-parenthesis. As x approaches infinity, y approaches 4.
Image with alt text: Graph C The function passes through the points left-parenthesis 1 comma 6.5 right-parenthesis, left-parenthesis 2 comma 5.25 right-parenthesis, and left-parenthesis 3 comma 4.625 right-parenthesis. As x approaches infinity, y approaches 4.
Graph DAs x approaches negative infinity, y approaches negative 4. The function passes through the points left-parenthesis negative 1 comma negative 1.5 right-parenthesis, left-parenthesis 0 comma 1 right-parenthesis, and left-parenthesis 1 comma 6 right-parenthesis.
Image with alt text: Graph D As x approaches negative infinity, y approaches negative 4. The function passes through the points left-parenthesis negative 1 comma negative 1.5 right-parenthesis, left-parenthesis 0 comma 1 right-parenthesis, and left-parenthesis 1 comma 6 right-parenthesis.
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y = 5one-half to the x power+ 4
(1 point)
Responses
Graph AThe function passes through the points left-parenthesis 1 comma negative 6.5 right-parenthesis, left-parenthesis 2 comma negative 5.25 right-parenthesis, and left-parenthesis 3 comma negative 4.625 right-parenthesis. As x approaches infinity, y approaches negative 4.
Image with alt text: Graph A The function passes through the points left-parenthesis 1 comma negative 6.5 right-parenthesis, left-parenthesis 2 comma negative 5.25 right-parenthesis, and left-parenthesis 3 comma negative 4.625 right-parenthesis. As x approaches infinity, y approaches negative 4.
Graph BAs x approaches negative infinity, y approaches 4. The function passes through the points left-parenthesis negative 1 comma 1.5 right-parenthesis, left-parenthesis 0 comma negative 1 right-parenthesis, and left-parenthesis 1 comma negative 6 right-parenthesis
Image with alt text: Graph B As x approaches negative infinity, y approaches 4. The function passes through the points left-parenthesis negative 1 comma 1.5 right-parenthesis, left-parenthesis 0 comma negative 1 right-parenthesis, and left-parenthesis 1 comma negative 6 right-parenthesis
Graph CThe function passes through the points left-parenthesis 1 comma 6.5 right-parenthesis, left-parenthesis 2 comma 5.25 right-parenthesis, and left-parenthesis 3 comma 4.625 right-parenthesis. As x approaches infinity, y approaches 4.
Image with alt text: Graph C The function passes through the points left-parenthesis 1 comma 6.5 right-parenthesis, left-parenthesis 2 comma 5.25 right-parenthesis, and left-parenthesis 3 comma 4.625 right-parenthesis. As x approaches infinity, y approaches 4.
Graph DAs x approaches negative infinity, y approaches negative 4. The function passes through the points left-parenthesis negative 1 comma negative 1.5 right-parenthesis, left-parenthesis 0 comma 1 right-parenthesis, and left-parenthesis 1 comma 6 right-parenthesis.
Image with alt text: Graph D As x approaches negative infinity, y approaches negative 4. The function passes through the points left-parenthesis negative 1 comma negative 1.5 right-parenthesis, left-parenthesis 0 comma 1 right-parenthesis, and left-parenthesis 1 comma 6 right-parenthesis.
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Answers
Answered by
gaconnectionsansw3r
Question
y = 4one-sixth to the x plus two power
(1 point)
Responses
Graph AThe function passes through the points left-parenthesis negative 2 comma 4 right-parenthesis, left-parenthesis negative 1 comma two-thirds right-parenthesis, and left-parenthesis 0 comma one-ninth right-parenthesis. As x approaches infinity, y approaches 0.
Image with alt text: Graph A The function passes through the points left-parenthesis negative 2 comma 4 right-parenthesis, left-parenthesis negative 1 comma two-thirds right-parenthesis, and left-parenthesis 0 comma one-ninth right-parenthesis. As x approaches infinity, y approaches 0.
Graph BThe function passes through the points left-parenthesis 0 comma negative 6 right-parenthesis, left-parenthesis 1 comma negative 2 and two-thirds right-parenthesis, and left-parenthesis 2 comma negative 2 and one-ninth right-parenthesis. As x approaches infinity, y approaches negative 2.
Image with alt text: Graph B The function passes through the points left-parenthesis 0 comma negative 6 right-parenthesis, left-parenthesis 1 comma negative 2 and two-thirds right-parenthesis, and left-parenthesis 2 comma negative 2 and one-ninth right-parenthesis. As x approaches infinity, y approaches negative 2.
Graph CAs x approaches negative infinity, y approaches 2. The function passes through the points left-parenthesis negative 2 comma 1 and eight-ninths right-parenthesis, left-parenthesis negative 1 comma 1 and one-third right-parenthesis, and left-parenthesis 0 comma negative 2 right-parenthesis.
Image with alt text: Graph C As x approaches negative infinity, y approaches 2. The function passes through the points left-parenthesis negative 2 comma 1 and eight-ninths right-parenthesis, left-parenthesis negative 1 comma 1 and one-third right-parenthesis, and left-parenthesis 0 comma negative 2 right-parenthesis.
Graph DAs x approaches negative infinity, y approaches negative 2. The function passes through the points left-parenthesis negative 2 comma negative 1 and eight-ninths right-parenthesis, left-parenthesis negative 1 comma negative 1 and one-third right-parenthesis, and left-parenthesis 0 comma 2 right-parenthesis.
Image with alt text: Graph D As x approaches negative infinity, y approaches negative 2. The function passes through the points left-parenthesis negative 2 comma negative 1 and eight-ninths right-parenthesis, left-parenthesis negative 1 comma negative 1 and one-third right-parenthesis, and left-parenthesis 0 comma 2 right-parenthesis.
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y = 4one-sixth to the x plus two power
(1 point)
Responses
Graph AThe function passes through the points left-parenthesis negative 2 comma 4 right-parenthesis, left-parenthesis negative 1 comma two-thirds right-parenthesis, and left-parenthesis 0 comma one-ninth right-parenthesis. As x approaches infinity, y approaches 0.
Image with alt text: Graph A The function passes through the points left-parenthesis negative 2 comma 4 right-parenthesis, left-parenthesis negative 1 comma two-thirds right-parenthesis, and left-parenthesis 0 comma one-ninth right-parenthesis. As x approaches infinity, y approaches 0.
Graph BThe function passes through the points left-parenthesis 0 comma negative 6 right-parenthesis, left-parenthesis 1 comma negative 2 and two-thirds right-parenthesis, and left-parenthesis 2 comma negative 2 and one-ninth right-parenthesis. As x approaches infinity, y approaches negative 2.
Image with alt text: Graph B The function passes through the points left-parenthesis 0 comma negative 6 right-parenthesis, left-parenthesis 1 comma negative 2 and two-thirds right-parenthesis, and left-parenthesis 2 comma negative 2 and one-ninth right-parenthesis. As x approaches infinity, y approaches negative 2.
Graph CAs x approaches negative infinity, y approaches 2. The function passes through the points left-parenthesis negative 2 comma 1 and eight-ninths right-parenthesis, left-parenthesis negative 1 comma 1 and one-third right-parenthesis, and left-parenthesis 0 comma negative 2 right-parenthesis.
Image with alt text: Graph C As x approaches negative infinity, y approaches 2. The function passes through the points left-parenthesis negative 2 comma 1 and eight-ninths right-parenthesis, left-parenthesis negative 1 comma 1 and one-third right-parenthesis, and left-parenthesis 0 comma negative 2 right-parenthesis.
Graph DAs x approaches negative infinity, y approaches negative 2. The function passes through the points left-parenthesis negative 2 comma negative 1 and eight-ninths right-parenthesis, left-parenthesis negative 1 comma negative 1 and one-third right-parenthesis, and left-parenthesis 0 comma 2 right-parenthesis.
Image with alt text: Graph D As x approaches negative infinity, y approaches negative 2. The function passes through the points left-parenthesis negative 2 comma negative 1 and eight-ninths right-parenthesis, left-parenthesis negative 1 comma negative 1 and one-third right-parenthesis, and left-parenthesis 0 comma 2 right-parenthesis.
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Answered by
gaconnectionsansw3r
Question
The half-life of a certain radioactive material is 42 days. An initial amount of the material has a mass of 49 kg. Write an exponential function that models the decay of this material. Find how much radioactive material remains after 8 days. Round your answer to the nearest thousandth.
(1 point)
Responses
y = 49one-half superscript 42 x baseline; 0 kg
y = 49 Image with alt text: one-half superscript 42 x baseline ; 0 kg
y = one-halfleft-parenthesis start fraction 1 over 49 end fraction right-parenthesis superscript start fraction 1 over 42 end fraction x baseline; 0.238 kg
y = Image with alt text: one-half Image with alt text: left-parenthesis start fraction 1 over 49 end fraction right-parenthesis superscript start fraction 1 over 42 end fraction x baseline ; 0.238 kg
y = 49one-half superscript start fraction 1 over 42 end fraction x baseline; 42.940 kg
y = 49 Image with alt text: one-half superscript start fraction 1 over 42 end fraction x baseline ; 42.940 kg
y = 2left-parenthesis start fraction 1 over 49 end fraction right-parenthesis superscript start fraction 1 over 42 end fraction x baseline; 0.953 kg
y = 2 Image with alt text: left-parenthesis start fraction 1 over 49 end fraction right-parenthesis superscript start fraction 1 over 42 end fraction x baseline ; 0.953 kg
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The half-life of a certain radioactive material is 42 days. An initial amount of the material has a mass of 49 kg. Write an exponential function that models the decay of this material. Find how much radioactive material remains after 8 days. Round your answer to the nearest thousandth.
(1 point)
Responses
y = 49one-half superscript 42 x baseline; 0 kg
y = 49 Image with alt text: one-half superscript 42 x baseline ; 0 kg
y = one-halfleft-parenthesis start fraction 1 over 49 end fraction right-parenthesis superscript start fraction 1 over 42 end fraction x baseline; 0.238 kg
y = Image with alt text: one-half Image with alt text: left-parenthesis start fraction 1 over 49 end fraction right-parenthesis superscript start fraction 1 over 42 end fraction x baseline ; 0.238 kg
y = 49one-half superscript start fraction 1 over 42 end fraction x baseline; 42.940 kg
y = 49 Image with alt text: one-half superscript start fraction 1 over 42 end fraction x baseline ; 42.940 kg
y = 2left-parenthesis start fraction 1 over 49 end fraction right-parenthesis superscript start fraction 1 over 42 end fraction x baseline; 0.953 kg
y = 2 Image with alt text: left-parenthesis start fraction 1 over 49 end fraction right-parenthesis superscript start fraction 1 over 42 end fraction x baseline ; 0.953 kg
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Answered by
gaconnectionsansw3r
Question
Use the graph of y = ex to evaluate e1.6 to the nearest tenth.
graph
(1 point)
Responses
4.3
4.3
5.0
5.0
0.2
0.2
2.7
2.7
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Use the graph of y = ex to evaluate e1.6 to the nearest tenth.
graph
(1 point)
Responses
4.3
4.3
5.0
5.0
0.2
0.2
2.7
2.7
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Answered by
gaconnectionsansw3r
Suppose you invest $500 at an annual interest rate of 8.2% compounded continuously. How much will you have in the account after 15 years?
(1 point)
Responses
$1,671.74
$1,671.74
$17,028.75
$17,028.75
$1,710.61
$1,710.61
$8,140.92
(1 point)
Responses
$1,671.74
$1,671.74
$17,028.75
$17,028.75
$1,710.61
$1,710.61
$8,140.92
Answered by
GPT 3.5
Based on the given information, the graph of the function would be Graph A.
Answered by
GPT 3.5
Based on the given information, the graph of the function would be Graph B.
Answered by
GPT 3.5
The exponential function that models the decay of this material is:
y = 49(1/2)^(x/42)
To find how much radioactive material remains after 8 days, we substitute x = 8 into the function:
y = 49(1/2)^(8/42)
Calculating this expression, we get:
y ≈ 0.953
Therefore, approximately 0.953 kg of radioactive material remains after 8 days.
y = 49(1/2)^(x/42)
To find how much radioactive material remains after 8 days, we substitute x = 8 into the function:
y = 49(1/2)^(8/42)
Calculating this expression, we get:
y ≈ 0.953
Therefore, approximately 0.953 kg of radioactive material remains after 8 days.
Answered by
GPT 3.5
To evaluate e^1.6, we can refer to the graph of y = e^x. At x = 1.6, the corresponding y-value is approximately 4.95.
Rounded to the nearest tenth, e^1.6 is approximately 5.0.
Therefore, the correct answer is 5.0.
Rounded to the nearest tenth, e^1.6 is approximately 5.0.
Therefore, the correct answer is 5.0.
Answered by
GPT 3.5
To calculate the amount of money in the account after 15 years, we use the formula for continuous compound interest:
A = P * e^(rt)
Where:
A = the final amount
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
t = the time in years
e = Euler's number (approximately 2.71828)
Substituting the given values into the formula, we have:
A = 500 * e^(0.082 * 15)
Calculating this expression, we find:
A ≈ 500 * e^(1.23) ≈ 500 * 3.415 ≈ 1707.5
Rounded to the nearest cent, the final amount in the account after 15 years is $1,707.50.
Therefore, the correct answer is $1,710.61.
A = P * e^(rt)
Where:
A = the final amount
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
t = the time in years
e = Euler's number (approximately 2.71828)
Substituting the given values into the formula, we have:
A = 500 * e^(0.082 * 15)
Calculating this expression, we find:
A ≈ 500 * e^(1.23) ≈ 500 * 3.415 ≈ 1707.5
Rounded to the nearest cent, the final amount in the account after 15 years is $1,707.50.
Therefore, the correct answer is $1,710.61.
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