Exponential/Logarithmic Functions

Front

What is an exponential function?

Back

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

Front

What is the general form of a logarithmic function?

Back

The general form of a logarithmic function is y = log_b(x), where 'b' is the base of the logarithm and 'x' is the argument.

Front

What is the relationship between exponential and logarithmic functions?

Back

Exponential functions and logarithmic functions are inverses of each other. If y = b^x, then x = log_b(y).

Front

What does it mean for a function to exhibit exponential growth?

Back

Exponential growth occurs when a quantity increases at a rate proportional to its current value, typically represented by a function of the form y = a * b^x where b > 1.

Front

What does it mean for a function to exhibit exponential decay?

Back

Exponential decay occurs when a quantity decreases at a rate proportional to its current value, typically represented by a function of the form y = a * b^x where 0 < b < 1.

Front

How do you find the y-intercept of an exponential function?

Back

The y-intercept of an exponential function y = a * b^x is found by evaluating the function at x = 0, which gives y = a.

Front

What is the domain of the function y = 2^x?

Back

The domain of the function y = 2^x is all real numbers, expressed as (-∞, ∞).

Front

What is the range of the function y = 2^x?

Back

The range of the function y = 2^x is all positive real numbers, expressed as (0, ∞).

Front

How do you evaluate log_5(25)?

Back

To evaluate log_5(25), you determine what power you raise 5 to in order to get 25. Since 5^2 = 25, log_5(25) = 2.

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.