Writing Exponential Equations

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What is an exponential equation?

Back

An exponential equation is an equation in which a variable appears in the exponent. It can be expressed in the form y = a(b^x), where a is a constant, b is the base, and x is the exponent.

Front

How do you write an exponential equation for a population that halves every day?

Back

The equation is y = a(1/2)^x, where a is the initial population and x is the number of days.

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What does the base of an exponential function represent?

Back

The base of an exponential function indicates the growth or decay factor. If the base is greater than 1, the function represents growth; if it is between 0 and 1, it represents decay.

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How do you determine the y-intercept of an exponential function?

Back

The y-intercept of an exponential function is found by evaluating the function at x = 0. For y = a(b^x), the y-intercept is y = a.

Front

What is the general form of an exponential growth equation?

Back

The general form of an exponential growth equation is y = a(b^x), where a > 0 and b > 1.

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What is the general form of an exponential decay equation?

Back

The general form of an exponential decay equation is y = a(b^x), where a > 0 and 0 < b < 1.

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How do you write an exponential equation for bacteria that triples every 2 hours?

Back

The equation is y = a(3)^(x/2), where a is the initial number of bacteria and x is the time in hours.

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

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The exponent in an exponential equation indicates the number of time intervals that have passed, affecting the growth or decay of the quantity.

Front

How do you convert a doubling time into an exponential equation?

Back

For a quantity that doubles every t hours, the equation is y = a(2)^(x/t), where a is the initial amount.

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What is the relationship between the base and the growth rate in an exponential function?

Back

The base of an exponential function determines the growth rate; a larger base results in faster growth.