Exam Activity Review of exponential functions

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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 a positive real number, and 'x' is the exponent. It shows rapid growth or decay.

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What does the base of an exponential function represent?

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The base of an exponential function determines the rate of growth or decay. If the base is greater than 1, the function grows; if it is between 0 and 1, the function decays.

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How do you write an exponential growth equation?

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An exponential growth equation can be written as y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

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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 interest is compounded per year, and t is the number of years.

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What does 'compounded quarterly' mean?

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Compounded quarterly means that interest is calculated and added to the principal four times a year.

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What is the initial value in the function f(x) = 300(1.16)^x?

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The initial value in the function f(x) = 300(1.16)^x is 300.

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How do you determine the total amount paid after a loan with compound interest?

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To determine the total amount paid after a loan with compound interest, use the compound interest formula and substitute the values for principal, rate, time, and compounding frequency.

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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 is greater than 1, leading to an increase over time. Exponential decay occurs when the base is between 0 and 1, leading to a decrease over time.

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How do you convert a percentage growth rate to a decimal for calculations?

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To convert a percentage growth rate to a decimal, divide the percentage by 100. For example, 14% becomes 0.14.

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What is the significance of the exponent in an exponential function?

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The exponent in an exponential function indicates the number of time periods that have passed, affecting the growth or decay of the function.