What is the value of $$f(3)$$ in the function $$f(x) = 1600(2)^x$$ ?

$$f(3) = 1600(2)^3 = 1600(8) = 12800$$ .

What is the difference between linear and exponential growth?

Linear growth increases by a constant amount, while exponential growth increases by a constant percentage, leading to much larger values over time.

What does the base of an exponential function indicate?

The base of an exponential function indicates the growth or decay rate; if the base is greater than 1, it indicates growth, and if it is between 0 and 1, it indicates decay.

How can you identify an exponential decay graph?

An exponential decay graph slopes downward and approaches the x-axis but never touches it, indicating that the quantity decreases over time.

What is the value of $$f(0)$$ in any exponential function $$f(x) = a(b)^x$$ ?

$$f(0) = a(b)^0 = a(1) = a$$ , meaning the value at x=0 is equal to the initial value $$a$$ .

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

The y-intercept of an exponential function is the initial value of the function when $$x = 0$$ , represented by $$f(0) = a$$ .

How do you determine if a sequence is exponential?

A sequence is exponential if each term is a constant multiple (the same ratio) of the previous term.

What is the equation for a function that represents exponential decay with a starting value of 5 and a decay factor of 0.5?

The equation is $$f(x) = 5(0.5)^x$$ .

Exponential Functions Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is an exponential function?

Back

2.

FLASHCARD QUESTION

Front

What does it mean for a function to exhibit exponential growth?

Back

Tags

CCSS.HSF-IF.C.8B

3.

FLASHCARD QUESTION

Front

What does it mean for a function to exhibit exponential decay?

Back

Tags

CCSS.HSF-IF.C.8B

4.

FLASHCARD QUESTION

Front

How do you calculate the value of an exponential function?

Back

Tags

CCSS.HSF-IF.C.8B

5.

FLASHCARD QUESTION

Front

What is the general form of an exponential growth function?

Back

6.

FLASHCARD QUESTION

Front

What is the general form of an exponential decay function?

Back

Tags

CCSS.HSF-IF.C.8B

7.

FLASHCARD QUESTION

Front

If a population doubles every year, what is the growth factor?

Back

The growth factor is 2, meaning the population multiplies by 2 each year.

Tags

CCSS.HSF-LE.A.1A

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