Writing 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 does the 'a' represent in an exponential function?

Back

The 'a' represents the y-intercept or initial value of the function.

Front

What is the base in an exponential function?

Back

The base is the constant 'b' in the function f(x) = a(b)^x, which determines the growth or decay rate.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base 'b' is greater than 1, while exponential decay occurs when the base 'b' is between 0 and 1.

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How do you identify the y-intercept of an exponential function?

Back

The y-intercept can be found by evaluating the function at x=0, which gives f(0) = a.

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What is the growth factor in an exponential growth function?

Back

The growth factor is the base 'b' in the function f(x) = a(b)^x when b > 1.

Front

What is the decay factor in an exponential decay function?

Back

The decay factor is the base 'b' in the function f(x) = a(b)^x when 0 < b < 1.

Front

If a function decreases by 29% each hour, what is the decay factor?

Back

The decay factor is 0.71, which represents the remaining amount after a 29% decrease.

Front

What is the general form of an exponential function?

Back

The general form is f(x) = a(b)^x, where 'a' is the initial value and 'b' is the base.

Front

How can you determine if a function is exponential from a graph?

Back

If the graph shows a curve that rises or falls rapidly and does not form a straight line, it is likely an exponential function.