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What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a consistent percentage over a period of time, represented by the function f(x) = a(b)^x, where b > 1.

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a consistent percentage over time, represented by the function f(x) = a(b)^x, where 0 < b < 1.

Front

What is a linear function?

Back

A linear function is a function that creates a straight line when graphed, represented by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the general equation for a linear function?

Back

The general equation for a linear function is y = mx + b.

Front

How do you identify exponential functions from a table of values?

Back

Exponential functions show a constant ratio between consecutive values, while linear functions show a constant difference.

Front

What does the variable 'x' represent in the function f(x) = a(b)^x?

Back

In the function f(x) = a(b)^x, 'x' represents the exponent, which indicates the number of time intervals or periods.

Front

What is the significance of the base 'b' in exponential functions?

Back

The base 'b' in exponential functions determines the growth (b > 1) or decay (0 < b < 1) rate of the function.

Front

If a penny is tripled every day, what type of function does this represent?

Back

This represents an exponential growth function.

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

How can you write an equation for exponential growth?

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An equation for exponential growth can be written as f(x) = a(b)^x, where a is the initial amount and b is the growth factor.