Exponential Functions

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 the base (a positive real number), and 'x' is the exponent.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base 'b' in the function f(x) = a * b^x is greater than 1, leading to an increase in value. Exponential decay occurs when 'b' is between 0 and 1, leading to a decrease in value.

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is f(x) = a * (1 + r)^x, where 'a' is the initial amount, 'r' is the growth rate, and 'x' is the time period.

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is f(x) = a * (1 - r)^x, where 'a' is the initial amount, 'r' is the decay rate, and 'x' is the time period.

Front

What does the base of an exponential function represent?

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The base of an exponential function represents the growth or decay factor. A base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Front

How do you identify exponential growth from a graph?

Back

Exponential growth is identified by a curve that rises steeply as 'x' increases, showing that the function's value increases rapidly.

Front

How do you identify exponential decay from a graph?

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Exponential decay is identified by a curve that falls steeply as 'x' increases, showing that the function's value decreases rapidly.

Front

What is the common ratio in an exponential sequence?

Back

The common ratio in an exponential sequence is the factor by which each term is multiplied to get the next term.

Front

If a savings account has an initial deposit of $500 and earns 4% interest compounded annually, what is the exponential function?

Back

f(x) = 500(1 + 0.04)^x.

Front

What is the value of f(3) if f(x) = 2(3)^x?

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f(3) = 2(3)^3 = 2 * 27 = 54.