Exponents and Exponentials

Front

What is an exponent?

Back

An exponent is a number that indicates how many times to multiply the base by itself. For example, in 2^3, 2 is the base and 3 is the exponent, meaning 2 is multiplied by itself 3 times (2 * 2 * 2 = 8).

Front

What does the term 'exponential growth' mean?

Back

Exponential growth refers to an increase that occurs at a rate proportional to the current value, resulting in a rapid rise over time. It can be represented by the function f(x) = a * b^x, where b > 1.

Front

What does the term 'exponential decay' mean?

Back

Exponential decay refers to a decrease that occurs at a rate proportional to the current value, leading to a rapid decline over time. It can be represented by the function f(x) = a * b^x, where 0 < b < 1.

Front

What is the common ratio in a geometric sequence?

Back

The common ratio is the factor by which each term in a geometric sequence is multiplied to get the next term. It can be found by dividing any term by the previous term.

Front

Evaluate: 3^0

Back

1 (Any non-zero number raised to the power of 0 is 1.)

Front

Evaluate: 5^1

Back

5 (Any number raised to the power of 1 is the number itself.)

Front

What does the 'b' represent in the exponential function f(x) = a * b^x?

Back

The 'b' represents the base of the exponential function, which determines the rate of growth (if b > 1) or decay (if 0 < b < 1).

Front

What is the value of 10^2?

Back

100 (10 multiplied by itself 2 times.)

Front

If f(x) = 2^x, what is f(3)?

Back

8 (2^3 = 2 * 2 * 2 = 8.)

Front

What is the graph of an exponential function with a base greater than 1?

Back

The graph shows exponential growth, rising steeply as x increases.