Question

f(40) n > 40
f(n) = f(1) + f(n-1)
f(40)= f(1) + f(40-1)
I'm lost from ^^ this point... help me figure out what to do from here...?

Answer 1

You have to work backwards. It's a recursive function.

I'll write out f(5) and maybe you'll see the pattern.

f(5)=f(1)+f(4) = 1 + 4 = 5
f(4) = f(1) +f(3) = 1 + 3 = 4
f(3) = f(2) + f(1) = 1 + 2 = 3
f(2) = f(1) +f(1) = 1 + 1 = 2

Answer 2

at least I think so

Answer 3

yea... no I don't get it....

Answer 4

basically, f(n) = n because of how the function is defined.

If we're given f(5), we need to find f(4), f(3), f(2), and f(1).

Answer 5

can you post the actual question so I can see where n>40 comes from

Answer 6

Bill is able to save $35/week after working part-time and paying his expenses. These two formulas show his weekly savings:
f(1) = 35, f(n) = f(1) + f(n-1) for n > 1
Use any formula of your choice to find f(40). Explain why you chose that method and what your answer means. Show your calculations.

does that make since?

Answer 7

f(5)=f(1)+f(4) = 35 + f(4) [using the formula definition]

but what is f(4)?

Answer 8

again, the definition for every f(n) is f(1) + f(n-1)

that means f(5) = f(1) + f(5-1) = f(1) + f(4)
and so, f(4) = f(1) + f(4-1) = f(1) +f(3)
f(3) = f(1) + f(3-1) = f(1) + f(2)
f(2) = f(1) + f(2-1) = f(1) + f(1)

And now we can finally work our way backwards.

f(1) = 35;
f(2) = f(1) + f(1) = 35 + 35 = 70
f(3) = f(1) + f(2) = 35 + 70 = 105
f(4) = f(1) + f(3) = 35 + 105 = 140

Do you see?

Answer 9

kinda sorta!
So with that pattern... I'd have to keep doing the same problem over and over and over again? till I got to f(40) ?

Answer 10

Ok... so I figured it out! and I wouldn't of done it with out your help! teehee thanks so much for your help!!!!! I finished my assignment with understanding!

Answer 11

Not really. There's a shortcut if you realize that f(n) = 35+ (n-1)*35

so f(40) = 35+ 39*35
=35 + 1365

Answer 12

Ooo ok coolio