Exponential Functions Review

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 base of an exponential function represent?

Back

The base of an exponential function determines the rate of growth or decay. If the base is greater than 1, the function represents exponential growth; if the base is between 0 and 1, it represents exponential decay.

Front

What is the multiplier in an exponential function?

Back

The multiplier is the base of the exponential function, which indicates how much the function value increases or decreases for each unit increase in x.

Front

What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a consistent percentage over time, resulting in a rapid increase as time progresses.

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What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a consistent percentage over time, leading to a rapid decrease as time progresses.

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How can you identify exponential growth on a graph?

Back

Exponential growth is identified on a graph by a curve that rises steeply to the right, indicating that the function value increases rapidly.

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How can you identify exponential decay on a graph?

Back

Exponential decay is identified on a graph by a curve that falls steeply to the right, indicating that the function value decreases rapidly.

Front

What is the general form of an exponential decay equation?

Back

The general form of an exponential decay equation is f(x) = a * (1 - r)^x, where 'a' is the initial amount and 'r' is the decay rate.

Front

What is the difference between linear functions and exponential functions?

Back

Linear functions have a constant rate of change, represented by a straight line, while exponential functions have a variable rate of change that increases or decreases exponentially.

Front

What does it mean if a graph is linear?

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A linear graph represents a linear function, where the relationship between the variables is constant, resulting in a straight line.