Exponential Graphs

Front

What is the y-intercept of an exponential function?

Back

The y-intercept is the point where the graph crosses the y-axis, represented as (0, f(0)). For example, in the function f(x) = a(b^x), the y-intercept is (0, a).

Front

What does it mean if a graph is classified as 'decay'?

Back

A decay graph shows a decrease in value as x increases. The function approaches zero but never touches it, indicating that the quantity is decreasing over time.

Front

How can you identify exponential growth in a function?

Back

Exponential growth occurs when the base of the exponent is greater than 1. For example, in the function A = 10(1.01)^x, the quantity increases as x increases.

Front

What is the general form of an exponential decay function?

Back

The general form is A = a(b^x), where 0 < b < 1. This indicates that the value decreases as x increases.

Front

What is the difference between exponential growth and decay?

Back

Exponential growth increases rapidly as x increases, while exponential decay decreases rapidly. Growth has a base greater than 1, and decay has a base between 0 and 1.

Front

What does the base of an exponential function represent?

Back

The base indicates the growth or decay factor. A base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Front

How do you find the y-intercept of the function f(x) = 2(1/7)^x?

Back

To find the y-intercept, evaluate f(0): f(0) = 2(1/7)^0 = 2(1) = 2. So, the y-intercept is (0, 2).

Front

What is an example of an exponential decay function?

Back

An example is f(x) = 5(0.5)^x, where the value halves as x increases.

Front

What does it mean for a function to be linear?

Back

A linear function has a constant rate of change and can be represented by a straight line on a graph, typically in the form f(x) = mx + b.

Front

What is the significance of the point (0, a) in an exponential function?

Back

The point (0, a) represents the initial value of the function when x = 0, which is the y-intercept.