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=\left(\frac{1}{3}\right)^{x - 3}-3), when (x = 0), (y=\left(\frac{1}{3}\right)^{- 3}-3=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}\approx - 2.89\neq2.037). For (y = 3^{x - 3}+2), when (x = 0), (y=3^{-3}+2=\frac{1}{27}+2=\frac{1 + 54}{27}\approx2.037). For (y=\left(\frac{1}{3}\right)^{x - 3}-2), when (x = 0), (y=\left(\frac{1}{3}\right)^{-3}-2=3^{3}-2=27 - 2 = 25\neq2.037).

Answer:

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