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 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

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

Back

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

Front

What is the common ratio in an exponential function?

Back

The common ratio is the factor by which the function's value multiplies for each unit increase in 'x'.

Front

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

Back

The common ratio is 4.

Front

Identify the common ratio in the sequence 3, 15, 75...

Back

The common ratio is 5.

Front

What type of function is f(x) = 2(1/7)^x?

Back

It is an exponential decay function.

Front

What type of function is f(x) = 2(0.85)^x?

Back

It is an exponential decay function.

Front

What type of function is y = 2(0.5)^x?

Back

It is an exponential decay function.