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Questions and Answers
What is the form of a linear function?
What is the equation for a quadratic function?
x^2 + x + 2
What is the form of an exponential function?
2 = 3^x
What is the initial amount (a) in the compound interest formula for $5,000 at 8% interest over 7 years?
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How many fruit flies are present after one day if there are 2 fruit flies that double every hour?
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How many fruit flies are present after 1 hour if there are 2 fruit flies that double every 20 minutes?
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What is the annual interest formula?
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What is the compound interest formula?
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What does the Product Property of logarithms state?
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What does the Quotient Property of logarithms state?
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What does the Power Property of logarithms state?
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What does the ExponentialLogarithmic Inverse Property state?
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What is the One to One Property of logs?
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What is the One to One Property of Exponents?
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Is there a solution for the equation $2^x = 6$?
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What is the value of $e^{ln2}$?
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What is the value of $e^{4ln2}$?
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What is the value of $ln(e)$?
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What is the continue form of the compound interest formula?
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How long will it take for an investment of $2,000 at 8% to double in value?
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If $e^x = 20$, what is the value of x?
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If $5^x = 20$, what is the value of x?
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Study Notes
Functions Overview
 Linear Function: Expressed as y = mx + b, where m represents the slope and b is the yintercept.
 Quadratic Function: Represented by the equation x^2 + x + 2; involves squared terms.
 Exponential Function: Formulated as 2 = 3^x, indicating rapid growth.
Interest Calculations
 Compound Interest Formula: A(t) = p(1 + r/n)^(nt), where p is the principal amount, r is the rate, n is the number of times interest is compounded per year, and t is the time in years.
 Annual Interest Formula: Similar to compound interest, expressed as y = ab^t, where ‘a’ is the initial amount, ‘b’ is the growth factor, and ‘t’ is time.
Examples of Growth
 Interest Example: Investing $5,000 at 8% interest over 7 years can be modeled using y = ab^t: a = 5,000, b = 1.08, t = 7.
 Fruit Fly Growth: Starting with 2 fruit flies that double every hour results in 2^24 flies after 24 hours using y = ab^t (a = 2, b = 2, t = 24).
 Fruit Fly Growth (Shorter Interval): If 2 fruit flies double every 20 minutes, this leads to y = ab^t with a = 2, b = 2, t = 3 (for 1 hour).
Logarithmic Properties
 Product Property: log(b)3 + log(b)5 = log(b)15; combines logarithms for multiplication.
 Quotient Property: log(b)2  log(b)1 = log(b)2; simplifies division within logarithms.
 Power Property: log(b)m^p = p * log(b)m; exponents pulled in front as a multiplier.
Inverse Properties
 ExponentialLogarithmic Inverse Property: log(b)b^x = x; connects logarithms and exponents.
 One to One Property of Logs: If log(b)x = log(b)y, then x must equal y; indicates uniqueness.
 One to One Property of Exponents: If b^x = b^y, then x must equal y; also denotes uniqueness.
Solutions and Limitations
 No Solution Case: For an equation like 2^x = 6, there is no solution as the base must be positive.
 Calculations with e: e^ln2 = 2 and e^(4ln2) = 16 by using properties of logarithms and exponents.
 Natural Logarithm: ln(e) = 1.
Time to Double Investment

Investment Doubling Time: For $2,000 at an 8% interest rate, to determine how long it takes to double:
 Set up the equation 4,000 = 2,000e^(0.08t) leading to t = ln2 / 0.08, resulting in approximately 8.66 years.
General Exponential Equations
 Exponential Equations: Equations such as e^x = 20 can be solved using natural logarithms, resulting in x = ln(20).
 Base Change: For equations like 5^x = 20, apply natural logarithm to isolate x: ln(5^x) = ln(20) results in x = ln(20)/ln(5).
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your understanding of key concepts from Algebra 2 Chapter 6 with these flashcards. Explore definitions and formulas related to linear, quadratic, and exponential functions. Perfect for reviewing and reinforcing your algebra skills.