U2 Exam Review

Front

What is exponential decay?

Back

Exponential decay refers to a decrease in quantity at a rate proportional to its current value, often represented by the function f(t) = a * e^(-kt), where 'a' is the initial amount, 'k' is the decay constant, and 't' is time.

Front

What is the general form of a linear function?

Back

The general form of a linear function is f(x) = mx + b, where 'm' is the slope and 'b' is the y-intercept.

Front

How do you determine if a function is exponential?

Back

A function is exponential if it can be expressed in the form f(x) = a * b^x, where 'a' is a constant, 'b' is a positive real number, and 'b' is not equal to 1.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the function; it indicates how much 'y' changes for a unit change in 'x'.

Front

What is the formula to calculate the slope between two points (x1, y1) and (x2, y2)?

Back

The formula for the slope (m) is m = (y2 - y1) / (x2 - x1).

Front

What is the value of a function at a specific point?

Back

The value of a function at a specific point x is found by substituting x into the function's equation.

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of 'b' in the equation f(x) = mx + b.

Front

What is the difference between linear and exponential functions?

Back

Linear functions have a constant rate of change, while exponential functions have a rate of change that increases or decreases exponentially.

Front

How do you find the equation of a line given a slope and a point?

Back

Use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is f(t) = a * e^(kt), where 'a' is the initial amount, 'k' is the growth constant, and 't' is time.