Exponential function

In mathematics, an exponential function is a function (or rule) that grows at a rapid rate.

Exponential functions follow the pattern $f(x)=a^{x}$ where a is a fixed real number, not equal to 0 (a Є R; a ≠ 0) and x is a variable real number (x Є R).

Exponential functions are named after the rate of growth they follow, as the results of the functions increase at a rapid, or exponential, rate.

Examples

One example of an exponential function in real life would be interest in a bank. If a person deposits £100 into an account which gets 3% interest a month then the balance each month would be (assuming the money is untouched):

Month	Balance	Month	Balance
January	£100.00	July	£119.41
February	£103.00	August	£122.99
March	£106.09	September	£126.68
April	£109.27	October	£130.48
May	£112.55	November	£134.39
June	£115.93	December	£138.42

Notice how the extra money from interest increases each month. The greater the original balance, the more interest the person will get.

Two mathematical examples of exponential functions are shown below.

a=2

$x$	Result
-2	0.25
-1	0.5
0	1
1	2
2	4
3	8
4	16

a=3

$x$	Result
-2	1/9
-1	1/3
0	1
1	3
2	9
3	27
4	81

bob is here dont fear