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 the exponential function f(x) = a * b^x?

Back

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

Front

How do you determine the y-intercept of the function y = 3^x?

Back

To find the y-intercept, set x = 0. Thus, y = 3^0 = 1, so the y-intercept is (0, 1).

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

What is the y-intercept of the function f(x) = 300(1.16)^x?

Back

The y-intercept is 300, which is the initial value when x = 0.

Front

If a function is represented as f(x) = 2(3)^x, is it exponential growth or decay?

Back

It is exponential growth because the base (3) is greater than 1.

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

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

Back

The base 'b' indicates the growth or decay factor; if b > 1, the function represents growth; if 0 < b < 1, it represents decay.

Front

How can you identify an exponential function from a graph?

Back

An exponential function graph will show a rapid increase or decrease, forming a curve that is not a straight line.

Front

What is the value of f(0) in the function f(x) = 5(2)^x?

Back

f(0) = 5(2)^0 = 5(1) = 5, so the value is 5.