Exponential Function Flashcard

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 a positive real number, and 'x' is the exponent.

Front

What is the horizontal asymptote of an exponential function?

Back

The horizontal asymptote of an exponential function is a horizontal line that the graph approaches as x approaches positive or negative infinity. For functions of the form f(x) = a * b^x, the horizontal asymptote is typically y = 0.

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'. It represents the initial value of the function.

Front

What is the difference between exponential growth and exponential decay?

Back

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

Front

How do you identify exponential growth from a graph?

Back

Exponential growth can be identified on a graph by a curve that rises steeply as x increases, indicating that the function's value increases rapidly.

Front

How do you identify exponential decay from a graph?

Back

Exponential decay can be identified on a graph by a curve that falls steeply as x increases, indicating that the function's value decreases rapidly.

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is f(x) = a * b^x, where 'a' is the initial value and 'b' > 1.

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is f(x) = a * b^x, where 'a' is the initial value and 0 < b < 1.

Front

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

Back

In an exponential function f(x) = a * b^x, the base 'b' represents the growth (if b > 1) or decay (if 0 < b < 1) factor of the function.

Front

What is the significance of the initial value 'a' in an exponential function?

Back

The initial value 'a' in an exponential function f(x) = a * b^x represents the value of the function when x = 0, indicating the starting point of the function.