M3: Unit 4 Review (Logs)

Front

What is the value of log₁₅1?

Back

0

Front

What is the formula for continuous exponential growth?

Back

y = A e^{kt}, where A is the initial amount, k is the growth rate, and t is time.

Front

How do you find the time it takes for a video to reach a certain number of views using the exponential growth model?

Back

Set the model equation equal to the target views and solve for t.

Front

What is the initial deposit in the formula A(t) = 6000e^{0.04t} + 2000?

Back

$8000

Front

What is the product rule for logarithms?

Back

log_b(xy) = log_bx + log_by

Front

How do you condense the expression log₃ + log_x?

Back

log(3x) using the product rule.

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.

Front

What is the change of base formula for logarithms?

Back

log_ba = log_ka / log_kb for any base k.

Front

What does it mean for a function to be exponential?

Back

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

Front

What is the natural logarithm?

Back

The natural logarithm is the logarithm to the base e, denoted as ln(x).