Introduction to 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 'a' represent in an exponential function?

Back

The 'a' represents the y-intercept, which is also the initial amount of the function.

Front

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

Back

The 'b' represents the growth or decay factor of the function.

Front

What is the difference between exponential growth and exponential decay?

Back

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

Front

How can you identify if a function is exponential growth or decay from its equation?

Back

If the base 'b' is greater than 1, it is exponential growth. If 'b' is between 0 and 1, it is exponential decay.

Front

Evaluate f(x) = 2(3)^x when x = 2.

Back

f(2) = 2(3)^2 = 2(9) = 18.

Front

What is the general form of an exponential function?

Back

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

Front

If f(x) = 4(2)^x, what is the y-intercept?

Back

The y-intercept is 4, which is the value of f(0).

Front

What happens to the graph of an exponential function as x approaches infinity?

Back

As x approaches infinity, the value of f(x) approaches infinity for exponential growth and approaches 0 for exponential decay.

Front

What is the value of f(x) = 5(0.5)^x when x = 3?

Back

f(3) = 5(0.5)^3 = 5(0.125) = 0.625.