What is the formula for the amount remaining after a certain time in exponential decay?

The formula is $$y = a \times b^t$$ , where 'a' is the initial amount, 'b' is the decay factor, and 't' is the time.

What is the decay factor in an exponential decay function?

The decay factor is the fraction of the quantity that remains after one time unit, often expressed as $$b = \frac{1}{2}$$ for half-life.

How do you determine the initial value in an exponential function?

The initial value is the value of 'y' when 'x' is 0, represented as 'a' in the function $$y = a \times b^x$$ .

What is the relationship between exponential functions and logarithms?

Exponential functions and logarithms are inverses of each other. The logarithm can be used to solve for the exponent in an exponential equation.

How do you graph an exponential function?

To graph an exponential function, plot points for various values of 'x', noting that the graph approaches the asymptote but never touches it.

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

Changing the base 'b' affects the steepness of the graph. A larger base results in a steeper curve for growth, while a smaller base (between 0 and 1) results in a slower decay.

What is an example of a real-world application of exponential functions?

Exponential functions are used in modeling population growth, radioactive decay, and compound interest in finance.

How can you write an exponential equation for a substance with a known half-life?

For a substance with a half-life of 'h', the equation can be written as $$y = a \times \frac{1}{2}^{\frac{x}{h}}$$ , where 'a' is the initial amount.

Exponential Functions Intro Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is an exponential function?

Back

2.

FLASHCARD QUESTION

Front

What does the term 'half-life' mean in the context of exponential decay?

Back

Half-life is the time required for a quantity to reduce to half its initial value. In exponential decay, it is the time taken for half of a substance to decay.

3.

FLASHCARD QUESTION

Front

What is the basic form of an exponential function?

Back

4.

FLASHCARD QUESTION

Front

What is the equation of the asymptote for exponential functions?

Back

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