Exponential Equations

Front

What is an exponential equation?

Back

An equation in which a variable appears in the exponent, typically in the form y = a(b^x), where a and b are constants.

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as x increases, the value of f(x) also increases.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing if, as x increases, the value of f(x) decreases.

Front

What is the general form of an exponential growth function?

Back

y = a(b^x) where b > 1.

Front

What is the general form of an exponential decay function?

Back

y = a(b^x) where 0 < b < 1.

Front

What is the domain of a function?

Back

The set of all possible input values (x-values) for the function.

Front

What is the range of a function?

Back

The set of all possible output values (y-values) for the function.

Front

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

Back

Set x = 0 in the function and solve for y.

Front

What is the y-intercept of the function f(x) = 4(2^x)?

Back

4, since f(0) = 4(2^0) = 4.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base of the exponent is greater than 1, while exponential decay occurs when the base is between 0 and 1.