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.

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What does it mean for a function to model exponential growth?

Back

Exponential growth occurs when a quantity increases by a constant percentage over equal time intervals, represented by a base greater than 1 in the function.

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What does it mean for a function to model exponential decay?

Back

Exponential decay occurs when a quantity decreases by a constant percentage over equal time intervals, represented by a base between 0 and 1 in the function.

Front

How do you identify the initial value in an exponential function?

Back

The initial value (or y-intercept) is the value of the function when x = 0, which is represented by the constant 'a' in the function f(x) = a(b)^x.

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Write an exponential function for a car worth $20,000 depreciating at 10% per year.

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V(t) = 20000(0.90)^t.

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Write an exponential function for an investment of $1,000 growing at 5% per year.

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B(t) = 1000(1.05)^t.

Front

What is the formula for exponential growth?

Back

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

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What is the formula for exponential decay?

Back

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

Front

If a population of bacteria doubles every 3 hours, how would you express this as an exponential function?

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P(t) = P0(2)^(t/3), where P0 is the initial population.

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What is the scale factor in an exponential function?

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The scale factor is the base of the exponential function, which determines the rate of growth (if > 1) or decay (if < 1).