4.1 Exponential Basics

Front

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 a positive real number, and x is the exponent.

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What does it mean for a function to exhibit exponential growth?

Back

Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to an increase that accelerates over time.

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CCSS.HSF-LE.A.1A

Front

What is the general form of an exponential growth function?

Back

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

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What is the difference between exponential growth and exponential decay?

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Exponential growth increases over time, while exponential decay decreases over time, typically represented by a function of the form f(x) = a(1 - r)^x.

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CCSS.HSF-IF.C.8B

Front

How do you simplify the expression 2^3 * 2^4?

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You can simplify it using the property of exponents: 2^3 * 2^4 = 2^(3+4) = 2^7.

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CCSS.8.EE.A.1

Front

What is the x-intercept of an exponential function?

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An exponential function does not have an x-intercept because it never touches the x-axis; it approaches zero but never reaches it.

Tags

CCSS.HSF-IF.C.7E

Front

What is the formula for compound interest?

Back

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.

Front

What is the base of an exponential function?

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The base of an exponential function is the constant factor that is raised to the power of the variable, typically denoted as b in the function f(x) = a * b^x.

Tags

CCSS.HSF-IF.C.8B

Front

How do you determine if a graph represents exponential growth or decay?

Back

A graph represents exponential growth if it rises steeply as x increases, and it represents exponential decay if it falls steeply as x increases.

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CCSS.HSF-IF.C.7E

Front

What is the significance of the constant 'e' in exponential functions?

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The constant 'e' (approximately 2.718) is the base of natural logarithms and is used in continuous growth or decay models, represented as f(x) = ae^(bx).

Tags

CCSS.HSF-IF.C.8B