APPC Unit 2A Review

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What is the formula for continuous compound interest?

Back

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

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How do you simplify expressions with exponents?

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To simplify expressions with exponents, use the laws of exponents: 1) a^m * a^n = a^(m+n), 2) a^m / a^n = a^(m-n), 3) (a^m)^n = a^(m*n), and 4) a^0 = 1.

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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 a positive real number, and x is the exponent.

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How do you determine the half-life of a substance?

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The half-life is the time required for a quantity to reduce to half its initial value. It can be calculated using the formula N(t) = N0 * (1/2)^(t/T), where N0 is the initial quantity, N(t) is the quantity at time t, and T is the half-life.

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What is the relationship between logarithms and exponents?

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Logarithms are the inverse operations of exponentiation. If b^y = x, then log_b(x) = y.

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How do you solve exponential equations?

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To solve exponential equations, you can take the logarithm of both sides or rewrite the equation in a form that allows you to isolate the variable.

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What is the value of 3^5?

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3^5 = 243.

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How do you calculate the amount of bacteria after a certain time given a half-life?

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To calculate the amount of bacteria after a certain time, use the formula N(t) = N0 * (1/2)^(t/T), where N0 is the initial number of bacteria, t is the total time, and T is the half-life.

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What is the formula for the amount of money in an account after t years with continuous compounding?

Back

The formula is A = Pe^(rt), where A is the amount, P is the principal, r is the interest rate, and t is the time in years.

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What does it mean for a function to be exponential?

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A function is exponential if it can be expressed in the form f(x) = a * b^x, where a is a constant and b is a positive real number.