which of the following exponential equations could be represented by the table below?\n|x| - 3| - 2|…

which of the following exponential equations could be represented by the table below?\n|x| - 3| - 2| - 1|0|1|2|3|4|5|\n|y|2.0014|2.0041|2.0123|2.037|2.111|2.333|3|5|11|\n\\(y = (\\frac{1}{3})^{x - 3}-3\\)\n\\(y = 3^{x - 2}-3\\)\n\\(y = 3^{x - 3}+2\\)\n\\(y = (\\frac{1}{3})^{x - 3}-2\\)

which of the following exponential equations could be represented by the table below?\n|x| - 3| - 2| - 1|0|1|2|3|4|5|\n|y|2.0014|2.0041|2.0123|2.037|2.111|2.333|3|5|11|\n\\(y = (\\frac{1}{3})^{x - 3}-3\\)\n\\(y = 3^{x - 2}-3\\)\n\\(y = 3^{x - 3}+2\\)\n\\(y = (\\frac{1}{3})^{x - 3}-2\\)

Answer

Explanation:

Step1: Test (x = 0) for each option

For (y = (\frac{1}{3})^{x - 3}-3), when (x = 0), (y=(\frac{1}{3})^{- 3}-3=27 - 3=24\neq2.037). For (y = 3^{x - 2}-3), when (x = 0), (y=3^{-2}-3=\frac{1}{9}-3=\frac{1 - 27}{9}=-\frac{26}{9}\neq2.037). For (y = 3^{x - 3}+2), when (x = 0), (y=3^{-3}+2=\frac{1}{27}+2=\frac{1 + 54}{27}=\frac{55}{27}\approx2.037). For (y = (\frac{1}{3})^{x - 3}-2), when (x = 0), (y=(\frac{1}{3})^{-3}-2=27 - 2 = 25\neq2.037).

Answer:

(y = 3^{x - 3}+2)