course pc 163 assignment #016016. `query 16
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13:52:56 `questionNumber 160000 behavior and source of exponential functions problem 1, perversions of laws of exponents Why is the following erroneous: a^n * b^m = (ab) ^ (n*m)
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RESPONSE --> When you plug in a^n*b^m=(ab)^(n*m) into numbers the answers are not equal. confidence assessment: 2
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13:53:04 `questionNumber 160000 STUDENT RESPONSE: my example was (4^2)(5^3) did not equal 20^6 INSTRUCTOR COMMENT ** more generally a^n * b^n = a^(n+m), which usually does not equal (ab) ^ (n * m) **
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RESPONSE --> I see. self critique assessment: 2
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13:54:18 `questionNumber 160000 Why is the follow erroneous: a^(-n) = - a^n
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RESPONSE --> It would be correct if a^(-n)= 1/a^n b/c both are positive but the way it is on the left makes one negative and one positive. confidence assessment: 2
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13:54:26 `questionNumber 160000 STUDENT RESPONSE: 2^-3 is not equal to -2^3 INSTRUCTOR COMMENT: ** A more general counterexample: a^(-n) = 1 / a^n is positive when a is positive whereas -a^n is negative when a is positive **
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RESPONSE --> I see. self critique assessment: 2
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13:54:57 `questionNumber 160000 Why is the following erroneous: a^n + a^m = a^(n+m)
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RESPONSE --> B/c whe you plug in the numbers the response was not equal. confidence assessment: 2
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13:55:05 `questionNumber 160000 STUDENT RESPONSE: (5^3)+(5^4) is not equal to 5^7 INSTRUCTOR COMMENT: (5^3) * (5^4) = (5^7) since (5*5*5) * (5*5*5*5) = 5*5*5*5*5*5*5 = 5^7. However (5^3) + (5^7) = 5*5*5 + 5*5*5*5*5 = 5*5*5( 1 + 5*5) = 5^3( 1 + 5^2), not 5^7.**
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RESPONSE --> I understand self critique assessment: 2
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13:59:48 `questionNumber 160000 STUDENT RESPONSE: Why is the following erroneous: a^0 = 0
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RESPONSE --> If you plug a number in for a say 5^0 it will not equal 0. self critique assessment: 2
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13:59:59 `questionNumber 160000 4^0 is not equal to 0 INSTRUCTOR COMMENT: ** a^(-n) * a^n = 0 but neither a^(-n) nor a^n need equal zero **
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RESPONSE --> I see. self critique assessment: 2
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14:01:32 `questionNumber 160000 Why is the following erroneous: a^n * a^m = a^(n*m).
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RESPONSE --> Because 5^8*5^2 doesnt equal %=5^16. confidence assessment: 2
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14:01:40 `questionNumber 160000 STUDENT RESPONSE: (4^7)(4^2) is not equal to 4^14 INSTRUCTOR COMMENT: Right. Generally a^n * a^m = a^(n+m), not a^(n*m).
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RESPONSE --> I see. self critique assessment: 2
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14:03:50 `questionNumber 160000 problem 2. Graph and describe Give basic points and asymptote; y values corresponding to the basic points, ratio of these y values: y = 1200 (2^(.12 t) )
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RESPONSE --> Basic points would be (0, 1200), and (1, 1304) it would be in negative x axis and the ratio wold approx. be 1.78 confidence assessment: 2
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14:04:00 `questionNumber 160000 STUDENT RESPONSE (0,1200),(1,1304) negative x-axis ratio=163/150 INSTRUCTOR COMMENT: the precise ratio is 2^.12, which is probably pretty close to 163/150
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RESPONSE --> i see self critique assessment: 2
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14:05:01 `questionNumber 160000 give basic points and asymptote; y values corresponding to the basic points, ratio of these y values: y = 400 ( 1.07 ) ^ t
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RESPONSE --> (0,400),(1,428) It would also be in the negative x axis and 1.07 would be ratio. confidence assessment: 2
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