Algebra 1 Exponential Review

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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 the base in an exponential function represent?

Back

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

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What is the initial amount in an exponential function?

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The initial amount is the value of 'a' in the function f(x) = a(b^x), representing the starting value when x = 0.

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How do you identify exponential growth?

Back

Exponential growth occurs when the base 'b' in the function f(x) = a(b^x) is greater than 1.

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How do you identify exponential decay?

Back

Exponential decay occurs when the base 'b' in the function f(x) = a(b^x) is between 0 and 1.

Front

What is the formula for calculating the amount after 't' years in an exponential growth model?

Back

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

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What is the formula for calculating the amount after 't' years in an exponential decay model?

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

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If a population grows by 20% each year, what is the growth factor?

Back

The growth factor is 1.20.

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If a bank account has an initial deposit of $500 and earns 5% interest compounded annually, what is the amount after 3 years?

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Using the formula A = P(1 + r)^t, A = 500(1 + 0.05)^3 = $578.81.

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What does it mean if a function is classified as exponential decay?

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It means that the quantity decreases over time, typically represented by a base less than 1 in the exponential function.