Exponential and Log Retake

Front

What is the general form of an exponential growth function?

Back

A = a(1 + r)^t, where A is the amount, a is the initial amount, r is the growth rate, and t is time.

Front

What is the general form of an exponential decay function?

Back

A = a(1 - r)^t, where A is the amount, a is the initial amount, r is the decay rate, and t is time.

Front

What does the base of an exponential function represent?

Back

The base indicates the growth or decay factor; a base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Front

What is an asymptote in the context of exponential functions?

Back

An asymptote is a line that a graph approaches but never touches; for exponential functions, the horizontal asymptote is typically y = 0.

Front

How do you determine if a function is exponential growth or decay?

Back

If the base of the exponential function is greater than 1, it is growth; if the base is between 0 and 1, it is decay.

Front

What is the relationship between logarithms and exponentials?

Back

Logarithms are the inverse operations of exponentials; if b^y = x, then log_b(x) = y.

Front

Evaluate log_4(1).

Back

0, because 4^0 = 1.

Front

What is the value of log_b(b)?

Back

1, because b^1 = b.

Front

What is the value of log_b(1)?

Back

0, because b^0 = 1.

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.