exponential functions

Project description
What are the key features of exponential functions? What are the key features of natural logs?

No need for references but perhaps a site about exponential functions or logs or something to make it look interesting and like i have “explored” the subject. Thanks!
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1.

Find derivatives of the functions defined as followed:

y= 3*4^x^2+2

2.
Prove that if y=y0e^kt, where y0 and k are constants then dy/dt=ky