Exponential growth functions (Algebra 1, Exponents and exponential functions) – Mathplanet

Exponential growth functions.

We have dealt with linear functions earlier. All types of equations containing two unknown (x and y) variables may be inserted in a coordinate system. These types of equations are known as functions. A straight line is known as a linear function . The function need not necessarily respond like a straight line equation. For example: If we have $50 000 deposited in the bank, and receive a 2 % interest annually, our investment shall increase as follows: Compare that with what we would have with a linear increase (2%): In this case we may note that the increase was constant each year. The investment may be described as: where x equals the number of years. However in the first case, the structure proceeds as: $$investment \:\: after \: x \: number \: of\: years$$ $$= initial\: capital \cdot compound\: interest^ $$ Here we have an x -variable in the exponent.

The interest and thus also the function are exponentials. Now we shall examine the differences displayed with the functions in our example above in a coordinate system. The lower straight line represents the linear increase and the upper bowed curve represents the exponential increase. In other words it is more profitable to have a compounded interest than a fixed return. An exponential function is a nonlinear function that has the form of. An exponential function with a > 0 and b > 1, like the one above, represents an exponential growth and the graph of an exponential growth function rises from left to right.