Exponential Functions (Alg 1 Honors)

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 indicate?

Back

The base of an exponential function indicates the growth or decay factor. 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 general form of an exponential growth function?

Back

The general form of an exponential growth function is f(t) = a * (1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Front

What is the general form of an exponential decay function?

Back

The general form of an exponential decay function is f(t) = a * (1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Front

How do you calculate the remaining amount of a substance after a certain time in exponential decay?

Back

To calculate the remaining amount, use the formula: Remaining Amount = Initial Amount * (1 - decay rate)^time.

Front

What does the term 'initial amount' refer to in exponential functions?

Back

The 'initial amount' refers to the starting value of the quantity being modeled before any growth or decay occurs.

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What is the significance of the exponent in an exponential function?

Back

The exponent indicates the number of time intervals that have passed, affecting the growth or decay of the function.

Front

How can you identify exponential growth from a graph?

Back

Exponential growth can be identified by a curve that rises steeply as it moves from left to right, indicating that the quantity increases rapidly.

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How can you identify exponential decay from a graph?

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Exponential decay can be identified by a curve that falls steeply as it moves from left to right, indicating that the quantity decreases rapidly.

Front

What is the difference between linear and exponential functions?

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Linear functions increase or decrease by a constant amount, while exponential functions increase or decrease by a constant percentage.