Exponentials & Rational Equations

A quantity that grows or decays by a fixed percent at regular intervals is said to possess exponential growth or decay, respectively.

Exponential growth is represented by the function y = a(1 + r)^t, while exponential decay is represented by the function y = a(1 − r)^t, where y is the new population, a is the initial population, r is the rate of growth or decay, and t is the number of time intervals that have elapsed.

A good strategy to use when solving radical equations is to square both sides of the equation. When doing so, however, be sure to check the solutions in the original equation, as you may end up with a root that is not a solution to the original equation.

When solving for a variable in an equation involving fractions, a good first step is to clear the variable out of the denominators of the fractions Remember that you can only multiply both sides of an equation by an expression when you know the expression cannot be equal to 0.