Exponential Functions - WORD PROBLEMS

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

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What does exponential growth mean?

Back

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

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What does exponential decay mean?

Back

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

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How do you identify exponential growth from a graph?

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Exponential growth graphs rise sharply and curve upwards, indicating that the rate of increase accelerates over time.

Front

How do you identify exponential decay from a graph?

Back

Exponential decay graphs fall sharply and curve downwards, indicating that the rate of decrease accelerates over time.

Front

What is the general form of an exponential decay equation?

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

Front

What is the general form of an exponential growth equation?

Back

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

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If a population of bacteria doubles every hour, what type of function does this represent?

Back

This represents exponential growth.

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If a car's value decreases by 15% each year, what type of function does this represent?

Back

This represents exponential decay.

Front

What is the initial value in an exponential function?

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The initial value is the starting amount before any growth or decay occurs, represented by 'a' in the equation.