EOC 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 the base (a positive real number), and 'x' is the exponent.

Front

What does the base 'b' in an exponential function represent?

Back

The base 'b' in an exponential function determines the rate of growth or decay. If b > 1, the function represents exponential growth; if 0 < b < 1, it represents exponential decay.

Front

How do you identify an exponential function from a table of values?

Back

An exponential function can be identified by a constant ratio of the outputs for equal increments in the inputs.

Front

What is the general shape of the graph of an exponential function?

Back

The graph of an exponential function rises rapidly (for b > 1) or falls rapidly (for 0 < b < 1) and approaches the x-axis but never touches it.

Front

What is the y-intercept of an exponential function?

Back

The y-intercept of an exponential function f(x) = a * b^x is the value of f(0), which equals 'a'.

Front

What is the domain of an exponential function?

Back

The domain of an exponential function is all real numbers, (-∞, ∞).

Front

What is the range of an exponential function with base b > 1?

Back

The range of an exponential function with base b > 1 is (0, ∞).

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base b > 1, leading to increasing values as x increases. Exponential decay occurs when 0 < b < 1, leading to decreasing values as x increases.

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 you to isolate the variable.

Front

What is a common application of exponential functions in real life?

Back

Exponential functions are commonly used to model population growth, radioactive decay, and interest calculations in finance.