Question

The table below shows the values of f(x) and g(x) for different values of x. One of the functions is a quadratic function, and the other is an exponential function. Which function is most likely increasing exponentially?xf(x)g(x)12225431084171652632 f(x), because it grows slower than g(x) f(x), because it eventually intersects g(x) g(x), because it grows faster than f(x) g(x), because it will not intersect f(x)

Answer 1

g(x), because it grows faster than f(x)

1) Given the table we can tell which one is follows an exponential model if we pick each output (f(x)) and divide it by its predecessor.

`\begin{gathered} g(x) \\ 4/2=2 \\ 8/4=2 \\ 16/8=2 \\ 32/16=2 \end{gathered}`

As we can see there is a constant factor between them.

2) Now, let's analyze the options. Exponential models start out with the same output by winding up surpassing the outputs of f(x), in a faster way than a quadratic would.

3) Thus, the answer is:

g(x), because it grows faster than f(x)