Does the table represent a linear or an exponential function? Explain.

Question

anonymous · Answer

x   1    2         3                4
	
y  16   64      256         1024

anonymous · Answer

Review the definition of linear and exponential. Linear means that for every increase in x (or decrease), y increase in a multiple of that x.
Exponential means that for every increase in x, y increase by a power of that amount.
What does your data tell you?

anonymous · Answer

@2le, So the answer would be its a linear function because it increases by

anonymous · Answer

16 x 4 = 64, 16 x 16 = 256  256 x 4 = 1024

anonymous · Answer

I suggest that you plot it on a graph and then you can see that the graph will curve up instead of being linear

anonymous · Answer

The equation for this is $$y=4*4^x$$

anonymous · Answer

so the answer would be its an exponential function and increases by

anonymous · Answer

If you look at my function, you'll notice that the x is a part of an exponent. the relationship between x and y has an exponent in it **hint hint**

anonymous · Answer

what does that mean, im not good at math

anonymous · Answer

It means that as x increase in value, the y value increases exponentially.
When x is 1, y is 16, then as x increases to 2, y increases exponentially to 64. This hints towards the system being exponential.

If it were linear, it'd be something like when x is 1, y is 16, then when x is 2, y is 32, and when x is 3, y is 64.

Notice how the rates of change is drastically different. Exponents have to potential to grow much faster.

anonymous · Answer

So @2le for my answer can i just write its a exponential fuction and increases (by such and such number)? 
It goes from multiply 4, to multiply 16, to multiply 4 is there a simplier form to write that?

anonymous · Answer

yes with exponents. it starts with 4*4 = 16, then 4*4*4 = 64 then 4*4*4*4 = 256 then 4*4*4*4*4 = 1024.
If you notice, when x=1 y=16 $$y=4*4^1$$ then x=2 y=64 $$y=4*4^2$$ then x=3 y=256 $$y=4*4^3$$ and finally x=4 y=2014 $$y=4*4^4$$

So the relationship between x and y is $$y=4*4^x$$

anonymous · Answer

Also @2le i should put its an exponential function because the numbers grow fast?

anonymous · Answer

Not because it grows fast, but because it grows at an exponential rate. The reason that y grows at an exponential rate is because the four is raised by an EXPONENT of x. The exponent (4 raised by the power of x) is the key in determining if this is an exponential function.

anonymous · Answer

thanks alot  @2le :)