O4C1 Non-Linear Functions (Exponential Functions)

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What is an exponential function?

Back

An exponential function is a mathematical function of the form y = a * b^x, where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent. It represents growth or decay depending on the value of 'b'.

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What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base 'b' in the function y = a * b^x is greater than 1, leading to an increase in value as 'x' increases. Exponential decay occurs when 'b' is between 0 and 1, resulting in a decrease in value as 'x' increases.

Front

What does the y-intercept of an exponential function represent?

Back

The y-intercept of an exponential function represents the initial value of the function when x = 0, which is equal to 'a' in the function y = a * b^x.

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

Back

An exponential function can be identified from a table of values if the ratio of consecutive outputs (y-values) is constant when the inputs (x-values) are increased by equal intervals.

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What is the general form of an exponential decay function?

Back

The general form of an exponential decay function is y = a * (1 - r)^x, where 'a' is the initial amount and 'r' is the decay rate (0 < r < 1).

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What is the base of an exponential function?

Back

The base of an exponential function is the constant 'b' in the function y = a * b^x, which determines the rate of growth or decay.

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What does it mean if a function is linear?

Back

A function is linear if it can be represented by a straight line on a graph, which means it has a constant rate of change and can be expressed in the form y = mx + b, where 'm' is the slope and 'b' is the y-intercept.

Front

How do you determine if a graph represents a linear or non-linear function?

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A graph represents a linear function if it forms a straight line. If the graph curves or has a changing slope, it represents a non-linear function.

Front

What is the significance of the initial value in an exponential function?

Back

The initial value in an exponential function indicates the starting amount before any growth or decay occurs, represented by 'a' in the function y = a * b^x.

Front

What is the formula for calculating the growth factor in an exponential function?

Back

The growth factor in an exponential function is calculated as (1 + r), where 'r' is the growth rate expressed as a decimal.