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

- anonymous

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- anonymous

Okay,
let's work on
Plan A

- anonymous

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

- anonymous

ok

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- anonymous

so
let's denote x for a day

- anonymous

Plan A
4000x+10,000

- anonymous

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

- anonymous

no

- anonymous

yes I do

- anonymous

that makes sense

- anonymous

Okay, let's move on to Plan B

- anonymous

The first day you make .01

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

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So notice for each day we are multiplying by 2

- anonymous

yes it doubles each day

- anonymous

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

- anonymous

Does that make sense

- anonymous

?

- anonymous

yes that does

- anonymous

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

- anonymous

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

- anonymous

make sense?

- anonymous

yes

- anonymous

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

- anonymous

that's fraction

- anonymous

ok, it is a long process by hand

- anonymous

that's why we use geometric series

- anonymous

ok which numbers do I enter in

- anonymous

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

- anonymous

that seems to be quit complicated

- anonymous

What is?

- anonymous

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

- anonymous

you are missing two digit at the end
2147483647

- anonymous

$21474836.48

- anonymous

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

- anonymous

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.)

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

add up each day

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