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 base 'b' in an exponential function represent?

Back

The base 'b' represents the growth (if b > 1) or decay (if 0 < b < 1) factor of the function.

Front

What is the general form of an exponential growth function?

Back

The general form is f(x) = a * b^x, where b > 1.

Front

What is the general form of an exponential decay function?

Back

The general form is f(x) = a * b^x, where 0 < b < 1.

Front

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

Back

The 'a' represents the initial value or the y-intercept of the function.

Front

How can you identify exponential growth from a graph?

Back

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

Front

How can you identify exponential decay from a graph?

Back

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

Front

What is the y-intercept of the function f(x) = 5 * 2^x?

Back

The y-intercept is 5, which is the value of f(0).

Front

If a population doubles every year, what type of function models this growth?

Back

This growth can be modeled by an exponential function.

Front

What is the effect of changing the base 'b' in an exponential function?

Back

Changing the base 'b' affects the rate of growth or decay; a larger base results in faster growth.