Linear, Exponential, or Neither?

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 a positive real number, and 'x' is the exponent. It shows rapid growth or decay.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and can be expressed in the form f(x) = mx + b, where 'm' is the slope and 'b' is the y-intercept.

Front

Which function type multiplies the same number each time?

Back

Exponential function.

Front

What does the graph of an exponential function look like?

Back

The graph of an exponential function is a curve that increases or decreases rapidly, often appearing to rise or fall steeply.

Front

What is the difference between linear and exponential growth?

Back

Linear growth increases by a constant amount, while exponential growth increases by a constant percentage, leading to much faster growth over time.

Front

Give an example of a real-world exponential function.

Back

The growth of bacteria, where the population doubles at regular intervals.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is y = mx + b.

Front

What is the slope in a linear function?

Back

The slope (m) represents the rate of change of the function, indicating how much 'y' changes for a unit change in 'x'.

Front

What is a characteristic of exponential decay?

Back

Exponential decay occurs when a quantity decreases at a rate proportional to its current value, often modeled as f(t) = a * e^(-kt).

Front

How can you identify an exponential function from a table of values?

Back

If the ratio of consecutive outputs (y-values) is constant, the function is exponential.