What is the difference between exponential growth and exponential decay?

Exponential growth occurs when the base $$b > 1$$ , leading to increasing values as $$x$$ increases. Exponential decay occurs when $$0

How do you write an exponential function given a specific point and the y-intercept?

Use the y-intercept to find $$a$$ and the specific point to find $$b$$ by substituting the values into the equation $$f(x) = a \times b^x$$ .

What is the formula to convert a table of values into an exponential function?

Use the form $$f(x) = a \times b^x$$ and solve for $$a$$ and $$b$$ using two points from the table.

What is the role of the constant $$a$$ in an exponential function?

The constant $$a$$ represents the initial value or the value of the function when $$x=0$$ .

How can you verify if a function is exponential using a table?

Check if the ratio of the outputs for equal increments in the inputs remains constant.

What is an example of an exponential function?

An example is $$f(x) = 3 \times 2^x$$ , which represents exponential growth.

How do you graph an exponential function?

Plot the y-intercept, then use the growth/decay factor to find additional points by calculating $$f(x)$$ for various values of $$x$$ .

What is the importance of understanding exponential functions in real life?

Exponential functions model real-world phenomena such as population growth, radioactive decay, and interest calculations.

Writing Exponential Functions from Tables & Graphs 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

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

Back

Look for a pattern where the ratio of consecutive outputs (y-values) is constant when the inputs (x-values) increase by the same amount.

Tags

CCSS.HSF-LE.A.1A

3.

FLASHCARD QUESTION

Front

What does the base of an exponential function represent?

Back

Tags

CCSS.HSF-IF.C.8B

4.

FLASHCARD QUESTION

Front

What is the general form of an exponential function?

Back

5.

FLASHCARD QUESTION

Front

How can you determine the equation of an exponential function from a graph?

Back

Tags

CCSS.HSF.LE.A.2

6.

FLASHCARD QUESTION

Front

What is the significance of the y-intercept in an exponential function?

Back

Tags

CCSS.HSF-IF.C.7E

7.

FLASHCARD QUESTION

Front

How do you find the growth factor in an exponential function?

Back

The growth factor can be found by dividing the output of the function at one point by the output at a previous point, given that the inputs differ by the same amount.

Tags

CCSS.HSF-IF.C.8B

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