Exponential Functions Part 1

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 graph of an exponential growth function look like?

Back

The graph of an exponential growth function rises sharply as x increases, showing a rapid increase in value.

Front

What does the graph of an exponential decay function look like?

Back

The graph of an exponential decay function falls sharply as x increases, approaching zero but never touching the x-axis.

Front

What is the growth factor in an exponential function?

Back

The growth factor is the base 'b' in the function f(x) = a * b^x, which indicates how much the function increases for each unit increase in x.

Front

What is the decay factor in an exponential function?

Back

The decay factor is the base 'b' in the function f(x) = a * b^x, where 0 < b < 1, indicating how much the function decreases for each unit increase in x.

Front

How do you identify exponential growth from a table of values?

Back

Exponential growth can be identified if the ratio of consecutive outputs (y-values) is constant and greater than 1.

Front

How do you identify exponential decay from a table of values?

Back

Exponential decay can be identified if the ratio of consecutive outputs (y-values) is constant and less than 1.

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 rapidly.

Front

What is an example of a real-world situation modeled by an exponential function?

Back

An example is population growth, where a population triples every year, modeled by an exponential function.

Front

What does it mean if a function has a negative growth factor?

Back

A negative growth factor indicates that the function is decreasing, which is characteristic of exponential decay.