Exponential Equations / Graphs

An exponential equation is an equation in which a variable appears in the exponent. For example, $$y = a \times b^x$$ , where 'a' is a constant, 'b' is the base, and 'x' is the exponent.

'a' represents the initial value or y-intercept of the function.

To find the y-intercept, set $$x = 0$$ in the function and solve for $$y$$ .

The general form is $$y = a \times b^x$$ , where 'a' is the initial value, 'b' is the growth factor, and 'x' is the exponent.

The growth factor is 1.15, which represents a 15% increase.

The y-intercept is (0, 18).

The starting value is 300.

The rate of change in exponential functions refers to how quickly the function's value increases or decreases, often represented by the base 'b'.

Linear growth increases by a constant amount, while exponential growth increases by a constant percentage.

A 20% decrease can be expressed with a growth factor of 0.8, as in $$y = a \times 0.8^x$$ .