9C, 9D 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 shows rapid growth or decay.

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What does the base 'b' represent in an exponential function?

Back

The base 'b' in an exponential function determines the rate of growth (if b > 1) or decay (if 0 < b < 1).

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How do you identify exponential growth?

Back

Exponential growth occurs when the base 'b' is greater than 1 in the function y = a(b^x).

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How do you identify exponential decay?

Back

Exponential decay occurs when the base 'b' is between 0 and 1 in the function y = a(b^x).

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What does 'a' represent in the equation y = a(1 + r)^t?

Back

In the equation y = a(1 + r)^t, 'a' represents the initial amount or principal before any growth or decay occurs.

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What is the formula for calculating exponential growth?

Back

The formula for exponential growth is y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is the time.

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What is the formula for calculating exponential decay?

Back

The formula for exponential decay is y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is the time.

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If a car's value is $15,000 and it depreciates at 8% per year, what is the exponential equation?

Back

The exponential equation is y = 15,000(0.92)^t.

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What does a 35% increase mean in terms of an exponential function?

Back

A 35% increase means that the function can be represented as y = a(1.35)^t, where 'a' is the initial amount.

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How do you convert a percentage rate to a decimal for exponential functions?

Back

To convert a percentage rate to a decimal, divide the percentage by 100. For example, 35% becomes 0.35.