Linear and 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 difference between linear and exponential growth?

Back

Linear growth increases by a constant amount over equal intervals, while exponential growth increases by a constant percentage over equal intervals.

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 f(x) = a * (1 - r)^x, where r is the decay rate.

Front

How can you identify an exponential growth graph?

Back

An exponential growth graph rises sharply and curves upwards, indicating that the rate of increase accelerates over time.

Front

How can you identify an exponential decay graph?

Back

An exponential decay graph falls sharply and curves downwards, indicating that the rate of decrease slows over time.

Front

What is the general form of an exponential decay equation?

Back

The general form is y = a * (1 - r)^x, where a is the initial amount and r is the decay rate.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line, represented by the equation f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is the slope in a linear function?

Back

The slope (m) represents the rate of change of the function, indicating how much y changes for a unit change in x.

Front

What does the y-intercept represent in a linear function?

Back

The y-intercept (b) is the value of y when x = 0, representing the starting point of the function on the y-axis.

Front

How do you write an equation for exponential growth?

Back

An equation for exponential growth can be written as y = a * (1 + r)^x, where a is the initial amount and r is the growth rate.