1. love_to_love_you

h of the following functions represents a geometric sequence? Why? a. The function f(x) = x^3 represents a geometric sequence because each term is cubed to make it greater. b. The function f(x) = 4x represents a geometric sequence because each term is the next higher multiple of 4. c. The function f(x) = 4x- 4 represents a geometric sequence because each term is 4 more than the previous term. d. The function f(x) = 4^x represents a geometric sequence because each term is 4 times as great as the previous term.

2. anonymous

soo what do u know about the sequence

3. anonymous

@jamesr lol she's off line

4. anonymous

ok less work 4 me

5. anonymous

@jamesr lol she's back

6. love_to_love_you

Sorry my computer died

7. love_to_love_you

Is it a?

8. SolomonZelman

9. SolomonZelman

An exponental function represents a geometric sequence. An exponential function is an form of: $$y=b^x$$ or $$y=a(b)^x$$

10. love_to_love_you

so it is A?

11. anonymous

-100 is the y intercept and if you change it 25 it would go up i believe it is a

12. SolomonZelman

it is not A.

13. SolomonZelman

An exponental function represents a geometric sequence. An exponential function is an form of: y=b$$^x$$ or y=a(b)$$^x$$ ---------------------------------------------------- why is this so that exponential function represents a geometric sequencet? A geometric sequence is a sequence that follows a pattern of multiplying. In other words you multiply the first term $$a_1$$ by common ratio $$\rm r$$ to get the the second term $$a_2$$. Then you multiply the second term $$a_2$$ by common ratio $$\rm r$$ to get to the third term $$a_3$$. (AND SO ON......) For example: $$3,~~6,~~12,~~24,~~48~...$$ You can see that the sequence starts from 3, so $$a_1=3$$ And that you multiply times 2, so $$\rm r$$=2. Now! We can represent the same thing exponentially.... how (read this while I am typing)

14. SolomonZelman

So, exponential function y=a(b)$$^x$$ (we will refer to the same example) we can write y=3(2)$$^{x-1}$$ and it will be equivalent. when x=1 you get: f(1)=3(2)$$^{1-1}$$ = 3(2)$$^{0}$$ =3 (and that is $$a_1$$) when x=2 you get: f(2)=3(2)$$^{2-1}$$ = 3(2)$$^{1}$$ =3•2=6 (and that is $$a_2$$) when x=3 you get: f(3)=3(3)$$^{3-1}$$ = 3(2)$$^{2}$$ =3•4=12 (and that is $$a_3$$) when x=4 you get: f(3)=3(3)$$^{4-1}$$ = 3(2)$$^{3}$$ =3•8=24 (and that is $$a_4$$) and so forth

15. love_to_love_you

So it is definitely not a. Could it be B or D?

16. SolomonZelman

do you know what arithemtic sequence is?

17. love_to_love_you

I'm leaning more towards b.

18. SolomonZelman

do you know what an arithmetic sequence is?

19. love_to_love_you

It's a sequence where the difference is constant

20. SolomonZelman

yes, where you add or subtract the same number.

21. anonymous

i have a feelin she guessin lol

22. SolomonZelman

And this (arithmetic sequence) is represented by linea function (in a form of y=mx+b)

23. SolomonZelman

linear*

24. love_to_love_you

You are not being any help Jamesr so if you do not have anything helpful to say, please leave.

25. SolomonZelman

So, option B y=4x when x=1, you get 4•1=4 when x=2, you get 4•2=8 when x=3, you get 4•3=12 when x=4, you get 4•4=16 when x=5, you get 4•5=25 so this function (for natural number x values) would represent an arithemtic sequence with the first term 4 and a common difference of 4.

26. SolomonZelman

And any other function in a form of y=mx+b is an arithmetic sequence (roughly speaking, of course)

27. SolomonZelman

So tell me now, is B the correct option or not?

28. love_to_love_you

Not

29. SolomonZelman

yes, B is not the answer.

30. love_to_love_you

And I'm guessing D isn't either.

31. SolomonZelman

why not?

32. love_to_love_you

Sorry *C and because its a form of mx+b

33. SolomonZelman

you need a function that represents a geometric sequence (not arithmetic sequence).

34. love_to_love_you

So d?

35. SolomonZelman

yes

36. love_to_love_you

Alrighty. Thanks!

37. anonymous

im sorry i was gonna help but @SolomonZelman beat me to it

38. anonymous

LOL @jamesr leave if you don't have nothing good ta say

39. anonymous

im sorry i am im just an donkey term some times

40. anonymous

LOL u said donkey