Question

PLZ HELP ASAP

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?



x f(x) g(x)
1 2 2
2 5 4
3 10 8
4 17 16
5 26 32
a
g(x), because it will not intersect f(x)
b
g(x), because it grows faster than f(x)
c
f(x), because it eventually intersects g(x)
d
f(x), because it grows slower than g(x)

Answer 1

the answer is B g(x) because it grows faster than f(x)

Explanation:

the numbers say that g(x) jump to higher ones faster causing that to be an exponential growth

Answer 2

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

Explanation:

First differences of f(x) have a difference of 2. This is characteristic of a quadratic function (second differences are constant).

First differences of g(x) have a ratio of 2, as do the terms of g(x). This is characteristic of an exponential function (terms and differences have a common ratio).

We note, too, that g(x) grows faster than f(x). An exponential function will grow faster than any polynomial function. An appropriate choice is ...

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