Question

Hard math question. Please help me.

Answer 1

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
f(n) = 35n
1) Which one of these formulas show the sequence written recursively, and which shows it written explicitly? Justify your explanations.
2) Use the recursive formula to make a table of values for 1 ≤ n ≤ 5. Show your calculations. Explain what your table means.
3) Use any formula of your choice to find f(40). Explain why you chose that method and what your answer means. Show your calculations.
4) Given the sequence of numbers: 5, 6, 8, 11, 15, 20, 26, 33, 41,… Explain whether or not this sequence can be considered a function.

Answer 2

@jim_thompson5910

Answer 3

@kirbykirby

Answer 4

@ganeshie8

Answer 5

@undeadknight26

Answer 6

@kirbykirby got this! Counting on you man!

Answer 7

So what are you thinking for the first part because it just really confuses me. @kirbykirby

Answer 8

try posting this in the math section, you'll probably get more help/quicker answers :)

Answer 9

Sorry I was afk for a bit. Looking at the question now..

Answer 10

1) f(1) = 35, f(n) = f(1) + f(n-1) for n > 1 is the recursive formula, because finding a certain value f(n) requires knowing the value of f(n-1), and that would require knowing the value for f(n-2), all the way to f(1). You do not get an immediate answer by just plugging in n=something. When you plug in n=something, you will get something that still depends on (n-1). The formula only stops recursing once you reach n=1.

The other one is explicit, because you immediately get a number when plug plug in a value for n.

2)
\(n=1\): then \(f(1)=35\). This is already given.
\(n=2: f(2)=f(1)+f(2-1)=35+f(1)=35+35=70\)
\(n=3: f(3)=f(1)+f(3-1)=35+f(2)=35+70=135\)
... continue the same logic until n=5
(Do you see the nature of the recursive formula now? If I want to know f(3) right away, I need to know the value of f(2), and f(2) requires knowing f(1) ! )

3) Based on question 2.. do you think it would be easier to find f(4) using the recursive formula, or the explicit formula??

Answer 11

f(40)*

Answer 12

Oops I definitely made a typo when I wrote 35 + 70 = 135, i meant 105 !

Answer 13

That's alright lol I knew what you meant

Answer 14

So for number three it would be easier to use the explicit formula

Answer 15

definitely ;)

Answer 16

Thank you so much!

Answer 17

np =]