Question

Bill is able to save $35/week after working part-time and paying his expenses. These two formulas show his weekly savings:
A. f(1) = 35, f(n) = f(1) + f(n-1) for n > 1
B. f(n) = 35n

1. Use the recursive formula to make a table of values for 1 ≤ n ≤ 5. Show your calculations.

2. 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 1

@jim_thompson5910

Answer 2

how far did you get with this one?

Answer 3

im still on part a

Answer 4

So
A. f(1) = 35, f(n) = f(1) + f(n-1) for n > 1
you mean?

Answer 5

yes, what do i do to get b?

Answer 6

f(1) = 35
what's f(2) equal to?

Answer 7

f(2)=70?

Answer 8

f(n) = f(1) + f(n-1)

f(2) = f(1) + f(2-1)

f(2) = f(1) + f(1)

f(2) = 35+35

f(2) = 70

correct

Answer 9

f(3) = ???

Answer 10

175?

Answer 11

f(n) = f(1) + f(n-1)

f(3) = f(1) + f(3-1)

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

f(3) = 35+70

f(3) = 105

Hopefully you are seeing how recursion works?

Answer 12

lol i dont know how i got 175

Answer 13

maybe you did 105+70

Answer 14

what is f(4)?

Answer 15

175

Answer 16

f(n) = f(1) + f(n-1)

f(4) = f(1) + f(4-1)

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

f(4) = 35 + 105

f(4) = 140

Answer 17

always go back to the given recursive definition

Answer 18

sorry i keep putting 70.

Answer 19

are we on part 1 yet?

Answer 20

1a, yes

Answer 21

we have one more, f(5)

Answer 22

175.00 finally

Answer 23

correct

Answer 24

make sure to put that all in a table for 1a

Answer 25

why am i making a table

Answer 26

It says so

1. Use the recursive formula to make a table of values for 1 ≤ n ≤ 5. Show your calculations.

Answer 27

i didnt see that but when were done with 1&2 then we got to do the second half, i forgot to post it. :/

Answer 28

well one thing at a time

Answer 29

I guess if it's part of the problem (part of #1 or #2), then it needs to be included

Answer 30

Income per week; Total after that week.

$35.00 Week one: $35.00
$35.00 Week two: $70.00
$35.00 Week three: $105.00
$35.00 Week Four: $140.00
$35.00 Week Five: $175.00

Answer 31

thats my table.?

Answer 32

That looks correct

Answer 33

III. calculations. Explain what your table means.
IV. Use any formula of your choice to find f(40). Explain why you chose that method and what your answer means. Show your calculations.
V. 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 34

you could calculate f(40) the recursive way

however that's very slow because you need f(1), f(2), f(3), ... etc etc all the way up to f(39) before you can even think of f(40)

Answer 35

the quicker way is to use f(n) = 35n

Answer 36

side note: notice how

Week three: $105.00

and how

f(n) = 35n
f(3) = 35*3
f(3) = 105

So the function in part B is a much faster way to calculate the table and any large value of n

Answer 37

So what number should i use for the up to 40 one?

Answer 38

you'd use n = 40, but I recommend you use f(n) = 35n

Answer 39

the method in part A is very slow to find f(40) or any large n value

Answer 40

I'll brb

Answer 41

so i times 35 by 40 everytime?

Answer 42

no that's just to calculate f(40)

Answer 43

is that bill gates.......??