linear vs exponential

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. The function grows rapidly as x increases.

Front

What is a linear function?

Back

A linear function is a mathematical function of the form f(x) = mx + b, where m is the slope and b is the y-intercept. It represents a straight line on a graph.

Front

How does an exponential function behave as x increases?

Back

An exponential function increases rapidly, often doubling or tripling in value over equal intervals, depending on the base of the exponent.

Front

How does a linear function behave as x increases?

Back

A linear function increases at a constant rate, meaning the change in y is consistent for equal changes in x.

Front

What is the common ratio in an exponential function?

Back

The common ratio in an exponential function is the factor by which the function's value multiplies for each unit increase in x.

Front

What is the difference between linear and exponential growth?

Back

Linear growth increases by a constant amount, while exponential growth increases by a percentage of the current value, leading to much faster growth over time.

Front

Write the equation for an exponential decay function with a starting value of 100 and a decay rate of 20%.

Back

f(x) = 100 * (0.8)^x.

Front

Write the equation for a linear function that starts at 5 and increases by 3 for each unit increase in x.

Back

f(x) = 3x + 5.

Front

What type of function describes the situation: A population of bacteria doubles every hour?

Back

Exponential function.

Front

What type of function describes the situation: A car travels at a constant speed of 60 miles per hour?

Back

Linear function.