Whats the function for the points (1,1) (2,3) (3,9) (4,27)

Question

anonymous · Answer

Will give medals and become fan!

anonymous · Answer

Look to see the progression and what they are

what do you know about  3, 9, 27 ? Hint: factor them if possible

anonymous · Answer

They each go up by multiplying 3

anonymous · Answer

yes. but if you factor them you can see the trend better if you show the exponents.

anonymous · Answer

I don't understand?

anonymous · Answer

$$ 3^0, 3^1, 3^2, 3^3, $$
what do you think the 5th element will look like?

anonymous · Answer

$$3^{4}$$

anonymous · Answer

and the 6th element? 
then the  $$x^{th}$$ element?

anonymous · Answer

$$3^{5}$$

anonymous · Answer

i dont know what $$x ^{th}$$

anonymous · Answer

S0 
$$y(0) = 3^0$$
$$y(1) = 3^1$$
$$y(2) = 3^2$$
$$y(5) = 3^5$$
So what is 
$$y(x)= ?$$

anonymous · Answer

$$y(6)=3^{6}$$

anonymous · Answer

Good! so lets ask what is y(x)? meaning if there is a variable what does the function look like. 
If $$y(6) = 3^6$$ 
the rule is whatever in the parentheses goes to the power on the three. 
What do you think y(x) looks like then?

anonymous · Answer

$$y(x)=3^{x}$$?

anonymous · Answer

Yes, but now the issue is that you need to connect 
$$y(1) = 3^0$$$$y(2) = 3^1$$$$y(3) = 3^2$$$$y(4) = 3^3$$
So now what is 
y(x)?
If the pattern is take what's in the parentheses, subtract 1 and put as the power?

anonymous · Answer

$$y(5)=3^{4}$$ ?

anonymous · Answer

yes! 
so your progression will be 
$$(1,3^0), (2,3^1), (3,3^2), ..., (5,3^4), (6, 3^5), ... (x, 3^?)$$
what is the question mark equal to.

anonymous · Answer

its equal to to x-1?

anonymous · Answer

Yes, so the function would be 
$$y=3^{x-1}$$