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 y-intercept represent in an exponential function?

Back

The y-intercept represents the initial value of the function when x = 0. It is found by evaluating f(0) = a(b)^0 = a.

Front

Identify the y-intercept in the function f(x)=13(0.27)^x.

Back

The y-intercept is 13.

Front

What is the common ratio in an exponential function?

Back

The common ratio (or multiplier) is the factor by which the function value changes for each unit increase in x. It is represented by the base 'b' in the function f(x) = a(b)^x.

Front

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

Back

The common ratio is 4.

Front

What is the initial value of the function f(x)=0.05(2)^x?

Back

The initial value is 0.05.

Front

How do you find the y-intercept of an exponential function?

Back

To find the y-intercept, substitute x = 0 into the function and solve for f(0).

Front

What is the common ratio for the sequence: 3, 15, 75...?

Back

The common ratio is 5.

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 base.

Front

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

Back

As x increases, the value of f(x) increases rapidly if b > 1, or decreases rapidly if 0 < b < 1.