Q2: Pre-AP Algebra 2 Retake on Flashcard#1 for Unit 1: L1.4-L1.5

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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 depending on the value of b.

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Define 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. The general form is A = A0 * (1 + r)^t, where A0 is the initial amount, r is the growth rate, and t is time.

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Define exponential decay.

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Exponential decay occurs when a quantity decreases by a consistent percentage over time, leading to a rapid decrease. The general form is A = A0 * (1 - r)^t, where A0 is the initial amount, r is the decay rate, and t is time.

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What does it mean for interest to be compounded quarterly?

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Compounding quarterly means that the interest on an investment or loan is calculated and added to the principal four times a year, resulting in interest being earned on previously accumulated interest.

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How do you calculate the total amount paid on a loan with compound interest?

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The total amount paid can be calculated using the formula A = P(1 + r/n)^(nt), where A is the total amount, P is the principal, 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 formula for exponential regression?

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The formula for exponential regression is typically expressed as y = ab^x, where y is the dependent variable, a is the initial value, b is the growth/decay factor, and x is the independent variable.

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What is the difference between compounded interest and simple interest?

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Compounded interest is calculated on the initial principal and also on the accumulated interest from previous periods, while simple interest is calculated only on the principal amount.

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How do you determine if a function represents growth or decay?

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To determine if a function represents growth or decay, look at the base of the exponential function: if the base is greater than 1, it represents growth; if the base is between 0 and 1, it represents decay.

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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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What is the formula for calculating the future value of an investment with compound interest?

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The future value (FV) can be calculated using the formula FV = P(1 + r/n)^(nt), where P is the principal, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.