PCX Chapter 3 Review

Front

What is the formula for continuous compound interest?

Back

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 the money is invested for in years.

Front

What is the value of log(100) in base 10?

Back

2, because 10^2 = 100.

Front

How do you solve the equation log(x) + log(8) = 2?

Back

Combine the logs: log(8x) = 2, then convert to exponential form: 8x = 100, so x = 12.5.

Front

What is the definition of a logarithm?

Back

A logarithm is the power to which a number must be raised to obtain another number. For example, log_b(a) = c means b^c = a.

Front

What is the change of base formula for logarithms?

Back

log_b(a) = log_k(a) / log_k(b), where k is any positive number.

Front

How do you solve for x in the equation 8^(x+1) = 3?

Back

Take the logarithm of both sides: (x+1)log(8) = log(3), then solve for x.

Front

What is the product property of logarithms?

Back

log_b(mn) = log_b(m) + log_b(n), which states that the log of a product is the sum of the logs.

Front

What is the quotient property of logarithms?

Back

log_b(m/n) = log_b(m) - log_b(n), which states that the log of a quotient is the difference of the logs.

Front

How do you solve the equation log_6(x) + log_6(x-5) = 2?

Back

Combine the logs: log_6(x(x-5)) = 2, then convert to exponential form: x(x-5) = 36, solve for x.

Front

What is the definition of exponential growth?

Back

Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to growth that accelerates over time.