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April 11th, 2019, 07:07 PM   #1
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From: tornto

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table difference

Create table of differences like the following to determine whether each relationship is linear, quadratic, exponential, or neither. Justify the answer.

Table image link:

https://imgur.com/a/HZvINpp


Please check whether my answers are right.


Table a):


Since the first and second differences are constant, it is a linear relationship.


Table b):


Since the ratio between y-value is constant, it's an exponential relationship.


Table c):

Since the second differences are constant and the first differences are not constant, it's a quadratic relationship.


Table d):

Since the second differences are constant and the first difference are not constant, it's a quadratic relationship.

Please check the answers. Also, please check the wording answers if better answer than my answer.


Thanks much.

Last edited by skipjack; April 12th, 2019 at 06:21 AM.
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April 12th, 2019, 06:58 AM   #2
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a) The first differences are a non-zero constant and the second differences are all zero, so the values are consistent with a linear relationship. By inspection, $y = 12x + 5$.

b) The y-values and the first differences have a non-zero ratio. This is consistent with an exponential relationship. By inspection, $y = 3^x$. The second differences aren't shown (ratios being shown instead, although differences were asked for).

c) The second differences are a non-zero constant, so the table is consistent with a quadratic relationship. By inspection, $y = 2x^2 - 3x + 5$.

d) The first differences are a non-zero constant and the second differences are all zero, so the values are consistent with a linear relationship. By inspection, $y = -5x - 2$.
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April 12th, 2019, 02:41 PM   #3
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From: tornto

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Thank you so much, yes D is A linear relationship.. i missed typed it.

For B):

The y is 3, 27, 243, 2187, 19683.
First difference = 24, 216, 1944, 17496. (Not 17676). correction
so the second table Second difference is 9, 9, 9
The relationship is Exponential, in first difference.

Regards

Dan

Last edited by yorkmanz; April 12th, 2019 at 02:55 PM.
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April 12th, 2019, 07:14 PM   #4
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b) The second differences should be 216 - 24 = 192, 1944 - 216 = 1728, and 17496 - 1944 = 15552.
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April 12th, 2019, 10:31 PM   #5
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Quote:
Originally Posted by skipjack View Post
b) The second differences should be 216 - 24 = 192, 1944 - 216 = 1728, and 17496 - 1944 = 15552.
Thanks for correcting me.

Regards

Dan
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