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

Front

What does the y-intercept of an exponential function represent?

Back

The y-intercept of an exponential function is the value of the function when x = 0, which is equal to 'a' in the function f(x) = a(b^x).

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base 'b' is greater than 1 (b > 1), while exponential decay occurs when the base 'b' is between 0 and 1 (0 < b < 1).

Front

How do you find the y-intercept of the function y = 3(4^x)?

Back

To find the y-intercept, substitute x = 0: y = 3(4^0) = 3(1) = 3.

Front

What is the starting term 'a' in the function f(x) = 300(1.16^x)?

Back

The starting term 'a' is 300, which represents the initial value of the function when x = 0.

Front

Identify the equation that represents exponential decay: y = 2000(0.88) or y = 0.5(1.88).

Back

The equation y = 2000(0.88) represents exponential decay because the base 0.88 is less than 1.

Front

Identify the equation that represents exponential growth: y = 2(0.5^x) or y = 0.5(2^x).

Back

The equation y = 0.5(2^x) represents exponential growth because the base 2 is greater than 1.

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is f(x) = a(b^x), where 'a' is the initial value and 'b' is the growth/decay factor.

Front

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

Back

The base 'b' indicates the growth or decay rate of the function; if b > 1, the function grows, and if 0 < b < 1, the function decays.

Front

How do you determine if a function is exponential?

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.