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 f(x) = a(b^x), where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent. It represents growth or decay processes.

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What does the base of an exponential function represent?

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

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How do you calculate the percent increase in a population modeled by an exponential function?

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The percent increase can be calculated by subtracting 1 from the base of the exponential function and multiplying by 100. For example, if P(t) = P_0(1 + r)^t, then the percent increase is r * 100.

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 (decimal), n is the number of times interest is compounded per year, and t is the number of years.

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If a population grows by 4% each year, what is the growth factor?

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The growth factor is 1.04, which represents a 4% increase.

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What is the difference between exponential growth and exponential decay?

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Exponential growth occurs when a quantity increases at a rate proportional to its current value, while exponential decay occurs when a quantity decreases at a rate proportional to its current value.

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How do you identify an exponential growth function from a graph?

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An exponential growth function will show a curve that rises steeply as x increases, indicating that the value of the function increases rapidly.

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What is the initial amount in the function f(x) = 10(0.3)^x?

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The initial amount is 10, which is the value of the function when x = 0.

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What does it mean if a function has a growth factor of 0.3?

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A growth factor of 0.3 indicates that the function represents exponential decay, meaning the quantity decreases to 30% of its previous value for each unit increase in x.

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How do you express a 35% increase in an exponential function?

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A 35% increase can be expressed as f(x) = initial amount * (1 + 0.35)^x, or f(x) = initial amount * (1.35)^x.