Linear and Exponential Functions

Front

What is a linear function?

Back

A linear function is a function that creates a straight line when graphed. It has the form f(x) = 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 in which an independent variable is in the exponent. It has the form f(x) = a(b^x), where a is a constant, b is the base, and x is the exponent.

Front

What does it mean for a function to exhibit exponential growth?

Back

Exponential growth occurs when a quantity increases by a consistent percentage over equal time intervals, resulting in a rapid increase.

Front

What does it mean for a function to exhibit exponential decay?

Back

Exponential decay occurs when a quantity decreases by a consistent percentage over equal time intervals, resulting in a rapid decrease.

Front

How do you write an equation for exponential growth?

Back

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

Front

How do you write an equation for exponential decay?

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The equation for exponential decay can be written as y = a(1 - r)^t, where a is the initial amount, r is the decay rate, and t is time.

Front

What is the difference between linear and exponential functions?

Back

Linear functions increase or decrease by a constant amount, while exponential functions increase or decrease by a constant percentage.

Front

What is the formula for calculating compound interest?

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The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the number of years.

Front

What is the y-intercept in 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 slope in a linear function?

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