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 is the common ratio in an exponential function?

Back

The common ratio (or growth factor) in an exponential function is the base 'b' in the function f(x) = a(b)^x.

Front

What does it mean if an exponential function has a base greater than 1?

Back

If the base 'b' is greater than 1, the function represents exponential growth.

Front

What does it mean if an exponential function has a base between 0 and 1?

Back

If the base 'b' is between 0 and 1, the function represents exponential decay.

Front

What is the x-intercept of an exponential function?

Back

An exponential function does not have an x-intercept; it approaches the x-axis but never touches it.

Front

How do you identify exponential growth on a graph?

Back

Exponential growth is identified by a curve that rises steeply as x increases.

Front

How do you identify exponential decay on a graph?

Back

Exponential decay is identified by a curve that falls steeply as x increases.

Front

What is the growth factor in the function f(x)=10(0.3)^x?

Back

The growth factor is 0.3.

Front

What is the formula for an exponential function?

Back

The formula for an exponential function is f(x) = a(b)^x, where 'a' is the initial value and 'b' is the base.

Front

What is the difference between linear and exponential functions?

Back

Linear functions have a constant rate of change, while exponential functions have a variable rate of change that increases or decreases multiplicatively.