Chapter 5 Exponentials and Logarithms Test Review

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What is the formula for continuous compounding of interest?

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The formula for continuous compounding is A = Pe^(rt), where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), and t is the time the money is invested for in years.

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How do you calculate the future value of an investment compounded annually?

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The future value 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 the money is invested.

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What is the logarithmic identity for converting between exponential and logarithmic forms?

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If b^y = x, then log_b(x) = y. This means that the logarithm of x with base b is equal to y.

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The value is 2, since 4^2 = 16.

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What does it mean for a logarithmic equation to have 'no solution'?

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A logarithmic equation has 'no solution' when the argument of the logarithm is negative or zero, which is not allowed in logarithmic functions.

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What is the relationship between the base of a logarithm and its inverse operation?

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The base of a logarithm indicates the number that must be raised to a power to obtain a given number. The inverse operation of a logarithm is exponentiation.

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Define 'compound interest'.

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Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods.

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What is the formula for calculating compound interest?

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The formula 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 (decimal), n is the number of times that interest is compounded per year, and t is the number of years.