Linear vs Exponential Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is an exponential function?

Back

An exponential function is a function of the form y = ab^x, where a is a constant, b is the base (a positive number), and x is the exponent. It represents growth or decay.

Front

What is the difference between linear and exponential growth?

Back

Linear growth increases by a constant amount, while exponential growth increases by a constant percentage, leading to faster growth over time.

Front

What is the equation for a linear function that starts at $100 and decreases by $5 each week?

Back

y = -5x + 100

Front

What type of function is represented by Uber's pricing model of $2 plus $0.75 per mile?

Back

Linear function.

Front

What is the formula for calculating exponential growth?

Back

The formula is P(t) = P0(1 + r)^t, where P0 is the initial amount, r is the growth rate, and t is time.

Front

What does it mean if a function is exponential decay?

Back

Exponential decay occurs when a quantity decreases at a rate proportional to its current value, often represented as y = ae^(-kt).

Front

How can you identify a linear function from a table of values?

Back

If the differences between consecutive y-values are constant as x increases, the function is linear.

Front

What is an example of exponential growth in real life?

Back

The population of a city growing by a fixed percentage each year is an example of exponential growth.

Front

What is the y-intercept in the equation y = 3x + 4?

Back

The y-intercept is 4, which is the value of y when x = 0.