Exponential Functions and Logarithms Test Review

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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.

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What does APR stand for?

Back

APR stands for Annual Percentage Rate, which is the annual rate charged for borrowing or earned through an investment.

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How do you calculate compound interest?

Back

Compound interest can be calculated using the formula 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 (decimal), n is the number of times that interest is compounded per year, and t is the number of years.

Front

What is the effective interest rate?

Back

The effective interest rate is the interest rate on a loan or financial product restated from the nominal interest rate as an interest rate with annual compound interest.

Front

Evaluate log_5(25).

Back

log_5(25) = 2, because 5^2 = 25.

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What is the base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power to obtain a certain value. For example, in log_b(a), b is the base.

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What is the difference between exponential growth and decay?

Back

Exponential growth occurs when a quantity increases at a rate proportional to its current value, while exponential decay occurs when a quantity decreases at a rate proportional to its current value.

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What is the formula for exponential growth?

Back

The formula for exponential growth is N(t) = N_0 * e^(rt), where N(t) is the amount at time t, N_0 is the initial amount, r is the growth rate, and e is Euler's number (approximately 2.71828).

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is N(t) = N_0 * e^(-rt), where N(t) is the amount at time t, N_0 is the initial amount, r is the decay rate, and e is Euler's number.

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What does it mean for a function to be increasing?

Back

A function is increasing if, as the input values increase, the output values also increase.