What is the general form of an exponential decay function?

The general form of an exponential decay function is $$f(x) = a \times b^x$$ , where $$0

If you triple your money every day, what is the exponential function that represents this situation?

The function is $$y = 5 \times 3^x$$ , where 5 is the initial amount.

In the function $$y = 24,220 \times (0.85)^x$$ , what does $$0.85$$ represent?

The number $$0.85$$ represents the decay factor, indicating that 15% of the investment is lost each month.

What is the difference between a growth factor and a decay factor?

A growth factor is greater than 1 (e.g., 1.05), while a decay factor is between 0 and 1 (e.g., 0.85).

What does the term 'asymptote' refer to in the context of exponential functions?

An asymptote is a line that a graph approaches but never touches; for exponential decay, the x-axis (y=0) is a horizontal asymptote.

How do you write an exponential function from a table of values?

Identify the initial value and the growth/decay factor by analyzing the ratio of consecutive values.

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

The base determines the rate of growth or decay; a larger base results in faster growth, while a smaller base (but greater than 0) results in faster decay.

What is the formula for calculating the amount after a certain time in an exponential growth situation?

The formula is $$A = P(1 + r)^t$$ , where $$A$$ is the amount after time $$t$$ , $$P$$ is the principal amount, $$r$$ is the growth rate, and $$t$$ is time.

Exponential Functions and Growth 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 it mean for an exponential function to represent growth?

Back

Tags

CCSS.HSF-IF.C.8B

3.

FLASHCARD QUESTION

Front

What does it mean for an exponential function to represent decay?

Back

Tags

CCSS.HSF-IF.C.8B

4.

FLASHCARD QUESTION

Front

How can you determine if an exponential function is growth or decay from its equation?

Back

Tags

CCSS.HSF-IF.C.8B

5.

FLASHCARD QUESTION

Front

What is the initial value in an exponential function?

Back

6.

FLASHCARD QUESTION

Front

Back

The number 14 represents the initial value of the function.

Tags

CCSS.HSF.LE.B.5

7.

FLASHCARD QUESTION

Front

What is the general form of an exponential growth function?

Back

Tags

CCSS.HSF-LE.A.1A

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