properties of exponential function ?

Question

a goood and not too long explanation. (grade 11 math) so don not go further than grade 11 math ; )

Answer 1

a function f(x) = a^x is said to be exponential function if the domain of x is set of real number and a is positive and the range of this function is set of positive ral number.

exponential function is said to be increasing if a>1 and function is decreasing if a<1
Exponential function becomes a constant function if a = 1

Answer 2

The exponential function has some great properties. You say 11th grade, does that include calculus?

If you have a graphing calculator it is instructive to graph it and take a look.

exp(x) is always positive
exp(0) is 1
lim at x-> -inf is 0
it is unbounded as x-> +inf

If you know calculus, it has the property that its derivative is equal to its value!

It shows up naturally in the solution of population equations. That is, the growth in a population depends on the size of the population. This is a differential equation whose solution yields the exponential functions.

I find wikipedia to be a great source of easily readable information for questions such as yours.

Answer 3

ITs derivative is an exponential function. It is always positve . It as the value 1 than the exponential term =0

Answer 4

The exponential function is one of the most important functions in mathematics. It is written as exp(x) or ex, where e equals approximately 2.71828183 and is the base of the natural logarithm.


HOPE THIS HELPS

Answer 5

It's a homomorphism grom the group of reals under addition to the group of positive reals under multiplication.

In other words,
a^(x+y)=a^x a^y.

It follows that
a^0=1
a^(-x)=1/a^x
and
[a^x]^n=a^(nx)