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 'a' represent in an exponential function?

Back

In an exponential function, 'a' represents the y-intercept, which is the value of the function when x = 0.

Front

What is the common ratio in an exponential function?

Back

The common ratio is the factor by which the function's value multiplies for each unit increase in x.

Front

How does an exponential function differ from a linear function?

Back

An exponential function grows or decays at a rate proportional to its current value, while a linear function grows at a constant rate.

Front

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

Back

The graph of an exponential function is a curve that either rises steeply (if b > 1) or falls steeply (if 0 < b < 1) as x increases.

Front

What does it mean if an amount triples each year?

Back

It means the growth is exponential, as the amount increases by a factor of 3 for each unit of time.

Front

If an amount increases by $10 each year, what type of function is this?

Back

This is a linear function, as the increase is constant.

Front

What is the rate of change in an exponential function?

Back

The rate of change in an exponential function is not constant; it increases or decreases exponentially based on the current value.

Front

What is the y-intercept of the function f(x) = 2 * 3^x?

Back

The y-intercept is 2, which is the value of the function when x = 0.

Front

What does it mean for a function to be neither linear nor exponential?

Back

It means the function does not exhibit constant growth (linear) or proportional growth (exponential), possibly showing a different type of relationship.