Modeling 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 y-intercept of a function?

Back

The y-intercept of a function is the value of y when x = 0. It is the point where the graph of the function crosses the y-axis.

Front

Identify the initial value in the function y = 6.87(4)^x.

Back

The initial value is 6.87, which is the value of y when x = 0.

Front

What does the letter 'b' represent in the linear equation y = mx + b?

Back

The letter 'b' represents the y-intercept or initial value of the linear function.

Front

What type of pattern do exponential functions have?

Back

Exponential functions grow or decay by multiplying or dividing by the same number (the base) for each unit increase in x.

Front

How do you identify an exponential function from a list of functions?

Back

An exponential function has a variable in the exponent, such as f(x) = 3^x, while polynomial functions have variables as bases.

Front

What is the general form of an exponential growth function?

Back

The general form is f(x) = a * b^x, where a > 0 and b > 1.

Front

What is the general form of an exponential decay function?

Back

The general form is f(x) = a * b^x, where a > 0 and 0 < b < 1.

Front

What is the difference between linear and exponential growth?

Back

Linear growth adds a constant amount, while exponential growth increases by a constant factor.

Front

What is the domain of an exponential function?

Back

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