Exponential Functions

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent.

Front

What does the base 'b' in an exponential function represent?

Back

The base 'b' represents the growth factor. If b > 1, the function represents exponential growth; if 0 < b < 1, it represents exponential decay.

Front

What is the general shape of the graph of an exponential growth function?

Back

The graph of an exponential growth function rises steeply as x increases, starting from a point above the x-axis.

Front

What is the general shape of the graph of an exponential decay function?

Back

The graph of an exponential decay function decreases rapidly and approaches the x-axis but never touches it.

Front

What does the 'a' represent in the exponential function f(x) = a * b^x?

Back

The 'a' represents the y-intercept of the function, which is the value of f(x) when x = 0.

Front

How do you identify exponential growth from a graph?

Back

Exponential growth can be identified by a curve that rises steeply to the right, indicating that the function's values increase rapidly.

Front

How do you identify exponential decay from a graph?

Back

Exponential decay can be identified by a curve that falls steeply to the right, indicating that the function's values decrease rapidly.

Front

What is the difference between linear and exponential functions?

Back

Linear functions increase or decrease by a constant amount, while exponential functions increase or decrease by a constant factor.

Front

What is the formula for calculating the value of an exponential function at a specific point?

Back

The value of an exponential function at a specific point x is calculated using f(x) = a * b^x.

Front

What is the common ratio in an exponential function?

Back

The common ratio is the factor by which the function's value multiplies as x increases by 1.