Exponential Equations

Front

What is an exponential equation?

Back

Front

What does the base of an exponential function represent?

Back

The base of an exponential function determines the rate of growth or decay. If the base is greater than 1, the function represents exponential growth; if the base is between 0 and 1, it represents exponential decay.

Front

What is the general form of an exponential function?

Back

Front

How do you identify exponential growth from a graph?

Back

Exponential growth is identified by a curve that rises steeply as x increases, indicating that the function's value increases rapidly.

Front

How do you identify exponential decay from a graph?

Back

Exponential decay is identified by a curve that falls steeply as x increases, indicating that the function's value decreases rapidly.

Front

What is the starting point of an exponential function?

Back

Front

What is the difference between linear and exponential functions?

Back

Linear functions have a constant rate of change, represented by a straight line, while exponential functions have a variable rate of change, represented by a curve.

Front

What does the term 'asymptote' mean in the context of exponential functions?

Back

An asymptote is a line that a graph approaches but never touches. For exponential decay, the x-axis (y=0) is a horizontal asymptote.

Front

How can you write an exponential function from a table of values?

Back

To write an exponential function from a table, identify the initial value and the growth/decay factor by examining the ratio of consecutive outputs.

Front

What is the significance of the initial value in an exponential function?

Back

The initial value (a) represents the starting amount before any growth or decay occurs, often found at x=0.