Question

I m having a hard time with this question. I cant figure out what the function would be for Plan A or Plan B

You get hired for a new job that will only last for one month (31 days, you work 7 days a week) and you are offered the two following payment plans to choose from:

• Plan A: $4,000 per day for the whole month with a $10,000 signing bonus.

• Plan B: $0.01 for day 1
$0.02 for day 2
$0.04 for day 3
$0.08 for day 4
$0.16 for day 5
….and so on
every day is double the previous days salary, with no signing bonus.

Create two functions that model each of these payment plans, wher

Answer 1

Okay,
let's work on
Plan A

Answer 2

notice that 4000 happen every day whereas 10,000 happen only once

Answer 3

ok

Answer 4

so
let's denote x for a day

Answer 5

Plan A
4000x+10,000

Answer 6

Do you understand how I got that before we move on to Plan B

Answer 7

no

Answer 8

yes I do

Answer 9

that makes sense

Answer 10

Okay, let's move on to Plan B

Answer 11

The first day you make .01

Answer 12

second day you make .01*(2)=.02
third day you make .01*(2)*(2)=.04

Answer 13

So notice for each day we are multiplying by 2

Answer 14

yes it doubles each day

Answer 15

second day you make .01*(2)=.02
third day you make .01*(2)*(2)= .01*(2)^2=.04
fourth day you make .01(2)*2*2=.01*(2)^3=.08

Answer 16

Does that make sense

Answer 17

?

Answer 18

yes that does

Answer 19

Okay , so you need to add what you make each day for whole month(31 days)

Answer 20

.01(2)^0+.01(2)^1+.01(2)^2+........+.01(2)^30
First day second third 31st day

Answer 21

make sense?

Answer 22

yes

Answer 23

You can add up all the term by hand, but it is very tedious. We can instead use a formula called Sum of Geometric Series
Our terms- .01(2^0+2^1+......+2^30)
r-2
n-30

Geometric Series Sum= \[[1-r^{n+1}]\over(1-r)\]

Answer 24

that's fraction

Answer 25

ok, it is a long process by hand

Answer 26

that's why we use geometric series

Answer 27

ok which numbers do I enter in

Answer 28

.01 * (1-(2)^31)/(1-2)

Answer 29

that seems to be quit complicated

Answer 30

What is?

Answer 31

I think I figured out how much the salary would be be in 31 days, $21474836

Answer 32

you are missing two digit at the end
2147483647

Answer 33

$21474836.48

Answer 34

* sorry, you are right, can't see the period

Answer 35

ok what is the function for plan B and here is more information for this question
(Plan A’s function, , will represent what you earn total over the whole 31 days, Plan B’s function, , will represent what you earn each individual day.)

Answer 36

Plan B function for each individual day =nth day= .01*(2)^(n-1)

Answer 37

Plan A's function A(t) and PLan B's function B(t),

Answer 38

ok so my question is how would i figure out the salary using that equation for plan B

Answer 39

add up each day