Exponential Equations

An equation in which a variable appears in the exponent, typically in the form y = a(b^x), where a and b are constants.

A function is increasing if, as x increases, the value of f(x) also increases.

A function is decreasing if, as x increases, the value of f(x) decreases.

y = a(b^x) where b > 1.

y = a(b^x) where 0 < b < 1.

The set of all possible input values (x-values) for the function.

The set of all possible output values (y-values) for the function.

Set x = 0 in the function and solve for y.

4, since f(0) = 4(2^0) = 4.

Exponential growth occurs when the base of the exponent is greater than 1, while exponential decay occurs when the base is between 0 and 1.