Respuesta :
The correct answers are:
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Answer choices:
________________
[B]: (1, 64)
[C]: (3, 16)
[D]: (8, 0.5)
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Explanation:
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For clarity, let us rewrite the problem as:
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F(x)=128* (0.5)ˣ
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Examine our answer choices;
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[all of which are given as ordered pairs: "(x, y)".].
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Start with the first "Answer Choice: [A]": (0, 1).
Is this correct?
(In other words, when "x" = 0; does "y" = 1 ?
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Looking at the problem:
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F(x)=128* (0.5)ˣ ; If x = 0, then y = 128.
(0.5)⁰ = 1 ; Then 128 * 1 = 128.
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So, answer choice: [A]: (0, 1): is incorrect).
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Now let us examine answer choice: [B]: (1, 64)
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Given our problem:
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F(x)=128* (0.5)ˣ ; When we substitute "1" for "x", do we get "64"?
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128 * (0.5)¹ =? 64? ; Note: (0.5)¹ = 0.5; so:
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128 * (0.5)¹ = 128 * (0.5) = 64 . Yes!
So this answer choice, "Answer choice: [B]: (1, 64)", is correct.
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Technically, there could be multiple correct answer choices, so let us examine the rest of the answer choices given:
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Let us examine answer choice: [C]: (3, 16) .
____________________________________________________________
Given: F(x)=128* (0.5)ˣ ; when we substitute "3" for "x", do we get "16"?
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Let us substitute "3" for "x"; and write as:
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F(x)=128 * (0.5)³ ; Note: (0.5)³ = 0.125 = 1/8 ; so:
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128 * (0.5)³ = 128 * 0.125 = 128 * (1/8) = 16. Yes.
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So this answer choice, "Answer choice: [C]: (3, 16)" is correct.
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Let us examine answer choice: [D]: (8, 0.5) .
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Given: F(x)=128* (0.5)ˣ ; when we substitute "8" for "x", do we get "0.5"?
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Let us substitute "8" for "x"; and write as:
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F(x)=128 * (0.5)⁸ ; Note: (0.5)⁸ = 0.00390625 = 1/256 ; so:
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128 * (0.5)⁸ = 128 * 0.00390625 = 128 * (1/256) = 0.5. Yes.
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So this answer, "Answer choice: [D]: (8, 0.5)" is correct.
_____________________________
Answer choices:
________________
[B]: (1, 64)
[C]: (3, 16)
[D]: (8, 0.5)
___________________________________________
Explanation:
___________________________________________
For clarity, let us rewrite the problem as:
___________________________________________
F(x)=128* (0.5)ˣ
___________________________________________
Examine our answer choices;
_________________________
[all of which are given as ordered pairs: "(x, y)".].
________________________________
Start with the first "Answer Choice: [A]": (0, 1).
Is this correct?
(In other words, when "x" = 0; does "y" = 1 ?
____________________________________
Looking at the problem:
____________________
F(x)=128* (0.5)ˣ ; If x = 0, then y = 128.
(0.5)⁰ = 1 ; Then 128 * 1 = 128.
____________________________
So, answer choice: [A]: (0, 1): is incorrect).
____________________________________
Now let us examine answer choice: [B]: (1, 64)
__________________________________________
Given our problem:
___________________________________________________
F(x)=128* (0.5)ˣ ; When we substitute "1" for "x", do we get "64"?
___________________________________________________
128 * (0.5)¹ =? 64? ; Note: (0.5)¹ = 0.5; so:
___________________________________________________
128 * (0.5)¹ = 128 * (0.5) = 64 . Yes!
So this answer choice, "Answer choice: [B]: (1, 64)", is correct.
___________________________________________________
Technically, there could be multiple correct answer choices, so let us examine the rest of the answer choices given:
_______________________________________________
Let us examine answer choice: [C]: (3, 16) .
____________________________________________________________
Given: F(x)=128* (0.5)ˣ ; when we substitute "3" for "x", do we get "16"?
________________________________________________
Let us substitute "3" for "x"; and write as:
________________________________________________
F(x)=128 * (0.5)³ ; Note: (0.5)³ = 0.125 = 1/8 ; so:
__________________________________________________
128 * (0.5)³ = 128 * 0.125 = 128 * (1/8) = 16. Yes.
__________________________________________________
So this answer choice, "Answer choice: [C]: (3, 16)" is correct.
__________________________________________________
Let us examine answer choice: [D]: (8, 0.5) .
__________________________________________________
Given: F(x)=128* (0.5)ˣ ; when we substitute "8" for "x", do we get "0.5"?
__________________________________________________
Let us substitute "8" for "x"; and write as:
________________________________________________
F(x)=128 * (0.5)⁸ ; Note: (0.5)⁸ = 0.00390625 = 1/256 ; so:
__________________________________________________
128 * (0.5)⁸ = 128 * 0.00390625 = 128 * (1/256) = 0.5. Yes.
________________________________________________
So this answer, "Answer choice: [D]: (8, 0.5)" is correct.
