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
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!
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.
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'....:)