We were to investigate on different functions. Let say there is a function y = 2^x and its derivative is 2^x ln 2.

We were suppose to fill the table below with the use of technology. Since were have not been taught derivative of natural logs. we can't use it.

And I know that when we divide dy/dx /y we get a number which is basically same as ln2.

I need help with my analysis and I have to make a conjecture by observing the pattern. And I am confused how can I show that 0.69314 is bascillay ln 2 without the use of derivative. (maybe with graph????)

x

y = 2x