Which exponential function is represented by the table? f(x) = 2(2x) f(x) = 0.8(0.8x) f(x) = 2(0.8x) f(x) = 0.8(2x)table-2 0.2-1 0.40 0.8 1 1.62 3.2

The answer is the last option, f(x) = 0.8 * (2^x)

The first strong indicator is that the fourth pair of data (0, 0.8) indicates that f(0) is 0.8

Given that a^0 = 1, means that the coefficient of the function has to be 0.8 and you discard the first and the third options, because for them two f(0) = 2.

AT the end what you have to do is to replace the values of x in equations and compare the results.

So, for the fourt opion you get:

x         f(x) = 0.8 * (2^x)

-2        0.8 * (2^-2) = 0.8 / 4 = 0.2

-1        0.8 * (2^-1) = 0.8 / 2 = 0.4

0         0.8 * (2^0) = 0.8 * 1 = 0.8

1         0.8 * (2^1) = 0.8 * 2 = 1.6

2          0.8 * (2^2) = 0.8 * 4 = 3.2

As you can see this results are the same of the table of the question, so the function is f(x) = 0.8 (2^x).