Why is e^x and its dy/dx so important whats it used for

i saw a video on math and they said that e^x and its derivative are extremely important in real life.

thanks 10 points for best explanation

One thing that is important about e^x, especially in Calculus, is that e^x is it's own derivative. This allows e^x to model stuff that has a growth rate present to the current value. For example, population is "usually" modeled using exponential functions since population rate "usually" grows at a rate proportional to the current population. You will see a lot more of this function later on in Calculus, trust me.

About the relationship between e^x and banking: recall that the compound interest formula says that after you deposit an amount P at an interest rate r compounded n times per year, then the amount in the bank account after t years is:
A = P(1 + r/n)^(nt).

If you let n --> infinity (in other words, compound the interest continuously), then the expression on the right side becomes Pe^(rt).

I hope this helps!

A lot of things in nature grow or decay at a rate proportional to their size. This can be written as a differential equation

dy/dt = k y

This can be rewritten as

dy/y = k dt

and the solution is

ln y = kt + c

y = C e^(kt)

This equation applies to money (dividends are proportional to principle), population growth, radioactive decay, capacitor charge, and many other phenomina.

Be patient your instructor will explain later.

so cuz derivation of e raise to x is same i.e e raise to x.....dat means whatever the condition is u mst remain same in real life same like ' e raise to x'....:)