Fan and Medal!!
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 3 3
2 6 9
3 11 27
4 18 81
5 27 243

f(x), because it eventually exceeds g(x)
g(x), because it eventually exceeds f(x)
f(x), because it eventually intersects g(x)
g(x), because it will not intersect f(x)

Question

Fan and Medal!!
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	3	3
2	6	9
3	11	27
4	18	81
5	27	243

 f(x), because it eventually exceeds g(x)
 g(x), because it eventually exceeds f(x)
 f(x), because it eventually intersects g(x)
 g(x), because it will not intersect f(x)

anonymous · Answer

I think its B but can you make sure? @SolomonZelman

solomonzelman · Answer

well, in g(x), you are multiplying each term by 3.
This is an geometric sequence.
3,9,27,81...
Geometric sequence is an exponential growth.

f(x) is perhaps some weird piece wise function (or at least the wa you typed it, that is a piece wise). (I would check the f(x)  )

it is not a sequence, nor geometric or arithmetic, so I won't think it is a function at all.

anonymous · Answer

So it would be D?

solomonzelman · Answer

g(x) is the exponential function, but is it because they don't intersect (and do they really not intersect?)  or is it because for bigger the x-values (I'll use your word) the g(x) exceeds the f(x) ?

anonymous · Answer

$f$ is quadratic, because the differences are successive odd numbers

solomonzelman · Answer

didn't know that rule..,ty

anonymous · Answer

in fact, it is pretty clearly $x^2+2$ check it

anonymous · Answer

Im so confused
@SolomonZelman  and  @satellite73

anonymous · Answer

@SolomonZelman  compute successive differences of any quadratic, as if you were finding the derivative 
$$f(x+1)-f(x)$$

anonymous · Answer

So it would be B ? @satellite73

anonymous · Answer

@Babyjoker001  it is no coincidence you are confused, the reasoning given for the possible answers is bogus
$f$ is a quadratic, and $g$ is exponential

solomonzelman · Answer

Sate, I'll work on that... tnx, got it on my paper.

anonymous · Answer

so they wouldnt intercept if their two different things...

anonymous · Answer

go with 
 g(x), because it eventually exceeds f(x)

anonymous · Answer

is this some FLVS  question perhaps?

anonymous · Answer

yes it is ... its so confusing to me

anonymous · Answer

how'd i guess? i keep asking for question id's so i can write to those morons and tell them how bad their questions are, but no one will ever provide one

solomonzelman · Answer

yes, b is wrong, because they intersect at (1,3) .
c is wrong. f(x) doesn't "eventually" intersect g(x). It intersects only in the beginning.
a is wrong, f(x) doesn't eventually exceed g(x),  (the other way) .

anonymous · Answer

actually B is right 
 g(x), because it eventually exceeds f(x)

anonymous · Answer

D is the one that says they do not intersect

anonymous · Answer

I know what you mean .... trust me some of the questions they ask is just plain insane ... @satellite73  and also do you mind if I fan u ?

solomonzelman · Answer

Ohh, I switched the order.

solomonzelman · Answer

srry abt dta