# Exponential Functions

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Exponential functions are the functions which involve variables and the base number, the only difference here in this case is that base is constant number and power is variable.  To evaluate this type of function, one needs to understand the basic concepts of exponents. The example of exponential function is 3^x, here in this case constant 3 is base and variable x is the exponent. The variable x can be positive or negative, both of these values helps to generate the graph of exponential functions in a very easy manner. This can be better clarified by the suitable relevant examples, and the examples are as follows:-

Question 1:- Tom invests \$200 at a bank that gives 5% compounded annually. With the help of general equation, frame an equation to model the growth of above investment.

Solution 1:- We know that,

General equation for this form is: - y = ab^x

Therefore y = ab^x = 200. (1.05)^x

Here, y is the money

And x is the number of years since the total investment.

Question 2:- Billy bought a new motor bike at a cost of \$30,000.  The motor bike depreciates 15% of its value each year. With the help of general equation, frame an equation to model the decay value of the motor bike.

Solution 2:-   We know that,

General equation for this form is: - y = ab^x

Therefore y = ab^x = 30,000 (1-0.15) ^x

So y = 30,000 (0.85) ^x

Here y is the value of the motor bike,

And x is basically the number of years since new purchase.