4.1 Exponential Basics

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What is exponential growth?

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Exponential growth occurs when a quantity increases by a consistent percentage over a period of time, resulting in a rapid increase that accelerates as time goes on.

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CCSS.HSF-LE.A.1A

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What is exponential decay?

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Exponential decay occurs when a quantity decreases by a consistent percentage over a period of time, leading to a rapid decrease that slows down as time progresses.

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CCSS.HSF-IF.C.8B

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What is the general form of an exponential function?

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The general form of an exponential function is f(x) = a(1 + r)^x, where 'a' is the initial amount, 'r' is the growth rate, and 'x' is the time.

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How do you identify exponential growth from a graph?

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Exponential growth is identified on a graph by a curve that rises steeply as it moves from left to right.

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CCSS.HSF-IF.C.7E

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How do you identify exponential decay from a graph?

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Exponential decay is identified on a graph by a curve that falls steeply as it moves from left to right.

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CCSS.HSF-IF.C.7E

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What does compounding mean in the context of exponential functions?

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Compounding refers to the process of earning interest on both the initial principal and the accumulated interest from previous periods.

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What is the difference between simple interest and compound interest?

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Simple interest is calculated only on the principal amount, while compound interest is calculated on the principal plus any interest that has already been added.

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CCSS.7.RP.A.3

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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 is the significance of the base in an exponential function?

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The base in an exponential function determines the rate of growth or decay; a base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

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CCSS.HSF-IF.C.8B

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What is an example of a real-world application of exponential functions?

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Real-world applications of exponential functions include population growth, radioactive decay, and compound interest in finance.