Exponetial Functions Test Review

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What is an exponential function?

Back

An exponential function is a mathematical function of the form y = a(b)^x, where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent. It shows rapid growth or decay.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base 'b' is greater than 1, leading to an increase in value as 'x' increases. Exponential decay occurs when the base 'b' is between 0 and 1, leading to a decrease in value as 'x' increases.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as 'x' approaches positive or negative infinity. For exponential functions, it often represents the value that the function approaches but never reaches.

Front

What is the initial value of an exponential function?

Back

The initial value of an exponential function is the value of the function when x = 0, represented by 'a' in the function y = a(b)^x.

Front

How do you identify an exponential function from an equation?

Back

An equation is an exponential function if it can be expressed in the form y = a(b)^x, where 'b' is a positive real number and 'b' is not equal to 1.

Front

What does it mean if the growth rate is greater than 1 in an exponential function?

Back

If the growth rate is greater than 1, the function exhibits exponential growth, meaning the value of the function increases rapidly as 'x' increases.

Front

What does it mean if the growth rate is less than 1 but greater than 0 in an exponential function?

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If the growth rate is less than 1 but greater than 0, the function exhibits exponential decay, meaning the value of the function decreases as 'x' increases.

Front

What is the equation of the horizontal asymptote for y = 8(0.88)^x?

Back

The horizontal asymptote is y = 0.

Front

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

Back

A function is exponential if its graph shows a rapid increase or decrease, forming a curve that approaches a horizontal line (asymptote) without touching it.

Front

What is the significance of the base 'b' in an exponential function?

Back

The base 'b' determines the rate of growth or decay. If b > 1, the function grows; if 0 < b < 1, the function decays.