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

Back

The letter 'b' represents the base of the exponential function, which determines the rate of growth or decay.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base 'b' is greater than 1, leading to an increase in value as x increases. Exponential decay occurs when the base 'b' is between 0 and 1, leading to a decrease in value as x increases.

Front

What is the y-intercept of an exponential function?

Back

The y-intercept of an exponential function f(x) = a * b^x is the value of f(0), which equals a.

Front

How do you identify an exponential function from a table of values?

Back

An exponential function can be identified if the ratio of consecutive outputs (y-values) is constant when the inputs (x-values) are increased by equal intervals.

Front

What is the general form of an exponential growth function?

Back

The general form of an exponential growth function is f(x) = a * b^x, where b > 1.

Front

What is the general form of an exponential decay function?

Back

The general form of an exponential decay function is f(x) = a * b^x, where 0 < b < 1.

Front

If a population doubles every year, what is the exponential function that represents this growth?

Back

The function is f(x) = a * 2^x, where 'a' is the initial population.

Front

What does the term 'y-intercept' mean in the context of a graph?

Back

The y-intercept is the point where the graph of a function crosses the y-axis, indicating the value of the function when x = 0.

Front

How can you determine if a function is exponential from its equation?

Back

A function is exponential if it can be expressed in the form f(x) = a * b^x, where 'a' is a constant and 'b' is a positive real number.