The exponential function, in the case of the natural exponential is f(x) = ex, where e is approximately 2.71828. The logarithmic function is the inverse of the exponential function. If we're talking about the natural logarithm (LN), then
y = LN(x), is the same as sayinig x = ey.
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fundamental difference between a polynomial function and an exponential function?
Ans: A natural log function ALWAYS has base e ( e is the irrational number that is the sum of the infinite series 2 + 1 / 2! + 1 /3! + 1 /4! + . . . )
y = ax, where a is some constant, is an exponential function in x y = xa, where a is some constant, is a power function in x If a > 1 then the exponential will be greater than the power for x > a
The linear function increases by the same number each step. The exponential function increases more each step. (1,1),(2,2),(3,3) etc (1,1).(2,4),(3,9),(4,16), etc see how the second one increases a lot?
Exponential growth is when the amount of something is increasing, and exponential decay is when the amount of something is decreasing.