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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Based on the given information, the graph of the function would be Graph A.
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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Based on the given information, the graph of the function would be Graph B.
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 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.
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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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.
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
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.