Writing Exponential Functions from Word Problems

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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

How do you identify exponential growth?

Back

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

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How do you identify exponential decay?

Back

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

Front

What does the initial value in an exponential function represent?

Back

The initial value is the value of the function when x = 0, represented by 'a' in the function f(x) = a(b)^x.

Front

In the function f(h) = 6(3)^h, what does '6' represent?

Back

The '6' represents the initial number of cells present before any growth occurs.

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What does the term 'rate of growth' mean in an exponential function?

Back

The rate of growth is the percentage increase applied to the initial value in an exponential growth function.

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What does the term 'rate of decay' mean in an exponential function?

Back

The rate of decay is the percentage decrease applied to the initial value in an exponential decay function.

Front

Write an exponential function for a quantity that triples every hour starting from 10.

Back

f(h) = 10(3)^h.

Front

If a function is modeled by f(x) = 200(0.9)^x, what does 0.9 represent?

Back

0.9 represents a 10% decay rate.

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How do you convert a percentage growth rate to a base for an exponential function?

Back

To convert a percentage growth rate 'r' to a base, use the formula b = 1 + r (as a decimal). For example, a 6% growth rate becomes b = 1 + 0.06 = 1.06.