U5D7: Review of Exponential Unit

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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 it mean for a function to have a growth factor?

Back

A growth factor indicates that the function's value increases as the input increases. In an exponential function, if the base 'b' is greater than 1, it represents growth.

Front

What does it mean for a function to have a decay factor?

Back

A decay factor indicates that the function's value decreases as the input increases. In an exponential function, if the base 'b' is between 0 and 1, it represents decay.

Front

How do you determine the transformation of a function?

Back

Transformations can be determined by analyzing changes in the function's equation, such as shifts (horizontal or vertical) and stretches or compressions.

Front

What is a vertical shift in a function?

Back

A vertical shift occurs when a constant is added or subtracted from the function, moving it up or down on the graph.

Front

What is a horizontal shift in a function?

Back

A horizontal shift occurs when a constant is added or subtracted from the input variable, moving the graph left or right.

Front

How do you calculate the population after a certain time with exponential growth?

Back

Use the formula y = a(2^(t/T)), where 'a' is the initial amount, 't' is the total time, and 'T' is the time it takes for the population to double.

Front

What is the doubling time in exponential growth?

Back

The doubling time is the period it takes for a quantity to double in size or value, often used in population growth models.

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is f(t) = a * e^(-kt), where 'a' is the initial amount, 'k' is the decay constant, and 't' is time.

Front

What is a vertical stretch in a function?

Back

A vertical stretch occurs when the output of the function is multiplied by a factor greater than 1, making the graph taller.