Math 3 EOC Review Mostly Logs

Front

What is the formula for calculating the margin of error in a sample mean?

Back

Margin of Error = Z * (σ/√n), where Z is the Z-score for the desired confidence level, σ is the standard deviation, and n is the sample size.

Front

How do you calculate the future value of an investment with compound interest?

Back

Future Value = P(1 + r/n)^(nt), where P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

Front

What is the definition of a logarithm?

Back

A logarithm is the exponent to which a base must be raised to produce a given number. For example, if b^y = x, then log_b(x) = y.

Front

How do you solve exponential growth problems?

Back

Use the formula 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 t is time.

Front

What is the relationship between logarithms and exponents?

Back

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

Front

Back

Front

What is the rule for solving equations with the same base?

Back

If a^x = a^y, then x = y, provided a > 0 and a ≠ 1.

Front

What is the formula for the standard deviation of a sample?

Back

Standard Deviation (s) = sqrt(Σ(x_i - x̄)² / (n - 1)), where x_i are the sample values, x̄ is the sample mean, and n is the sample size.

Front

How do you find the mean of a data set?

Back

Mean = (Σx_i) / n, where Σx_i is the sum of all data points and n is the number of data points.

Front

What is the definition of compound interest?

Back

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