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?

Back

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.

Back

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.

Tags

CCSS.HSF-LE.A.1A

Front

Define exponential decay.

Back

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.

Tags

CCSS.HSF-IF.C.8B

Front

What does it mean for interest to be compounded quarterly?

Back

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?

Back

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.

Tags

CCSS.HSF-LE.A.1A

Front

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.

Tags

CCSS.HSF-IF.C.8B

Front

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

Back

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.

Tags

CCSS.HSF-IF.C.8B

Front

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

Back

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.