Exponential Functions 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 the base (a positive real number), and 'x' is the exponent. It describes growth or decay processes.

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What does the base in an exponential function represent?

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The base in an exponential function represents the growth (if greater than 1) or decay (if between 0 and 1) factor of the function.

Tags

CCSS.HSF-IF.C.8B

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How do you convert a percentage to a decimal?

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To convert a percentage to a decimal, divide the percentage by 100. For example, 4.3% becomes 0.043.

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What is the formula for exponential growth?

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

Tags

CCSS.HSF-IF.C.8B

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What is the formula for exponential decay?

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

Tags

CCSS.HSF-IF.C.8B

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What is the y-intercept of an exponential function?

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The y-intercept of an exponential function is the value of 'y' when 'x' is 0, which is equal to 'a' in the function y = a(b^x).

Tags

CCSS.HSF-IF.C.7E

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If a population decreases by 6% per year, what is the decay factor?

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The decay factor is 1 - 0.06 = 0.94.

Tags

CCSS.HSF-LE.A.1C

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How do you find the population after a certain number of years with exponential decay?

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Use the formula P = P0(1 - r)^t, where P0 is the initial population, r is the decay rate, and t is the number of years.

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What does it mean if a function is exponential?

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A function is exponential if it can be expressed in the form y = a(b^x), indicating that the rate of change is proportional to the value of the function itself.

Tags

CCSS.HSF-LE.A.1A

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What is the difference between linear and exponential growth?

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Linear growth increases by a constant amount, while exponential growth increases by a constant percentage, leading to faster growth over time.