Exponential Key Features

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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

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

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The base 'b' represents the growth factor in an exponential function. If b > 1, the function represents exponential growth; if 0 < b < 1, it represents exponential decay.

Front

What is the general form of an exponential growth function?

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The general form of an exponential growth function is f(x) = a(1 + r)^x, where 'r' is the growth rate.

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What is the general form of an exponential decay function?

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The general form of an exponential decay function is f(x) = a(1 - r)^x, where 'r' is the decay rate.

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

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The y-intercept of an exponential function f(x) = a(b)^x is found by evaluating f(0), which equals a.

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What is the y-intercept of the function f(x) = 5(2)^x?

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The y-intercept is 5, since f(0) = 5(2)^0 = 5.

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What does it mean if an exponential function has a base greater than 1?

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If an exponential function has a base greater than 1, it indicates that the function is experiencing exponential growth.

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What does it mean if an exponential function has a base between 0 and 1?

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If an exponential function has a base between 0 and 1, it indicates that the function is experiencing exponential decay.

Front

How can you identify exponential growth or decay from a graph?

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Exponential growth graphs rise steeply to the right, while exponential decay graphs fall steeply to the right.

Front

What is the formula for compound interest?

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The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the number of years.