Exponential Functions

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where 'a' is a constant, 'b' is a positive real number, and 'x' is the exponent.

Front

What is the base of an exponential function?

Back

The base of an exponential function is the constant 'b' in the function f(x) = a * b^x, which determines the rate of growth or decay.

Front

What is exponential growth?

Back

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

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases at a rate proportional to its current value, leading to a rapid decrease over time.

Front

How do you solve an exponential equation?

Back

To solve an exponential equation, you can take the logarithm of both sides or rewrite the equation in a form that allows for easier manipulation.

Front

What is the formula for continuous compound interest?

Back

The formula for continuous compound interest is A = Pe^(rt), where A is the amount, P is the principal, r is the rate, and t is time.

Front

What is the value of 2^3?

Back

2^3 = 8.

Front

If f(x) = 3(2^x), what is f(4)?

Back

f(4) = 3(2^4) = 3(16) = 48.

Front

What is the inverse of an exponential function?

Back

The inverse of an exponential function is a logarithmic function.

Front

How do you express 27^(2x) = 3^(x-7) in terms of the same base?

Back

27 can be expressed as 3^3, so 27^(2x) = (3^3)^(2x) = 3^(6x). Thus, the equation becomes 3^(6x) = 3^(x-7).