Logarithms and Exponentials Test Review

Front

What is the natural logarithm of a number?

Back

The natural logarithm (ln) is the logarithm to the base e, where e is approximately equal to 2.71828. It is used to solve equations involving exponential growth or decay.

Front

If lnx = -3, what is the value of x?

Back

x = e^(-3) ≈ 0.0498.

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, r is the annual interest rate, and t is the time in years.

Front

How do you calculate the time it takes for an investment to triple with continuous compounding?

Back

Use the formula: t = (ln(3) / r), where r is the interest rate.

Front

What is the doubling time in continuous growth?

Back

The doubling time can be calculated using the formula: t = ln(2) / r, where r is the growth rate.

Front

If a population of bacteria doubles every 3 days, what is the daily growth rate?

Back

The daily growth rate can be found using the formula: r = (ln(2) / 3) * 100% ≈ 23%.

Front

What is an asymptote in a graph?

Back

An asymptote is a line that a graph approaches but never touches. It can be vertical, horizontal, or oblique.

Front

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 given number. For example, in log_b(x), b is the base.

Front

How do you find the vertical asymptote of a logarithmic function?

Back

Set the argument of the logarithm to zero and solve for x. For example, for y = log_b(x - 1), the vertical asymptote is at x = 1.

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.