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 starting term in the function f(x) = 300(1.16)^x?

Back

The starting term is 300.

Front

Identify the common ratio in the function f(x) = 2(4)^x.

Back

The common ratio is 4.

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 graph of an exponential growth function look like?

Back

The graph rises steeply as x increases, showing rapid growth.

Front

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

Back

The graph falls steeply as x increases, approaching zero but never touching the x-axis.

Front

What is the equation that best represents the graph of an exponential function?

Back

y = b^x, where b is the base of the exponential function.

Front

What is the difference between exponential growth and linear growth?

Back

Exponential growth increases at a rate proportional to its current value, while linear growth increases by a constant amount.