Exponential/Logarithmic Review

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What is an exponential function?

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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 depending on the value of b.

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What is the difference between exponential growth and exponential decay?

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Exponential growth occurs when the base of the exponential function (b) is greater than 1, leading to an increase over time. Exponential decay occurs when 0 < b < 1, resulting in a decrease over time.

Tags

CCSS.HSF-IF.C.8B

Front

What is the logarithmic form of an exponential equation?

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The logarithmic form of an exponential equation a^b = c is log_a(c) = b, where a is the base, b is the exponent, and c is the result.

Tags

CCSS.HSF.BF.B.5

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How do you convert an exponential equation to logarithmic form?

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To convert an exponential equation to logarithmic form, identify the base, the exponent, and the result, then use the format log_base(result) = exponent.

Tags

CCSS.HSF.BF.B.5

Front

What is the value of log_4(64)?

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The value of log_4(64) is 3, because 4^3 = 64.

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What is the value of log_3(81)?

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The value of log_3(81) is 4, because 3^4 = 81.

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How do you solve for x in the equation log_4(x) = 3?

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To solve for x, convert to exponential form: x = 4^3 = 64.

Tags

CCSS.HSF.BF.B.5

Front

What is the formula for exponential growth?

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The formula for exponential growth is A = P(1 + r)^t, where A is the amount after time t, P is the initial amount, r is the growth rate, and t is time.

Tags

CCSS.HSF-IF.C.8B

Front

What is the formula for exponential decay?

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The formula for exponential decay is A = P(1 - r)^t, where A is the amount after time t, P is the initial amount, r is the decay rate, and t is time.

Tags

CCSS.HSF-IF.C.8B

Front

If a population is 3400 and grows at 3% per year, what is the equation for the population after t years?

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The equation is A = 3400(1.03)^t.

Tags

CCSS.HSF.LE.A.2