anonymous
  • anonymous
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
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
Okay, let's work on Plan A
anonymous
  • anonymous
notice that 4000 happen every day whereas 10,000 happen only once
anonymous
  • anonymous
ok

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anonymous
  • anonymous
so let's denote x for a day
anonymous
  • anonymous
Plan A 4000x+10,000
anonymous
  • anonymous
Do you understand how I got that before we move on to Plan B
anonymous
  • anonymous
no
anonymous
  • anonymous
yes I do
anonymous
  • anonymous
that makes sense
anonymous
  • anonymous
Okay, let's move on to Plan B
anonymous
  • anonymous
The first day you make .01
anonymous
  • anonymous
second day you make .01*(2)=.02 third day you make .01*(2)*(2)=.04
anonymous
  • anonymous
So notice for each day we are multiplying by 2
anonymous
  • anonymous
yes it doubles each day
anonymous
  • 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
  • anonymous
Does that make sense
anonymous
  • anonymous
?
anonymous
  • anonymous
yes that does
anonymous
  • anonymous
Okay , so you need to add what you make each day for whole month(31 days)
anonymous
  • anonymous
.01(2)^0+.01(2)^1+.01(2)^2+........+.01(2)^30 First day second third 31st day
anonymous
  • anonymous
make sense?
anonymous
  • anonymous
yes
anonymous
  • 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
  • anonymous
that's fraction
anonymous
  • anonymous
ok, it is a long process by hand
anonymous
  • anonymous
that's why we use geometric series
anonymous
  • anonymous
ok which numbers do I enter in
anonymous
  • anonymous
.01 * (1-(2)^31)/(1-2)
anonymous
  • anonymous
that seems to be quit complicated
anonymous
  • anonymous
What is?
anonymous
  • anonymous
I think I figured out how much the salary would be be in 31 days, $21474836
anonymous
  • anonymous
you are missing two digit at the end 2147483647
anonymous
  • anonymous
$21474836.48
anonymous
  • anonymous
* sorry, you are right, can't see the period
anonymous
  • 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
  • anonymous
Plan B function for each individual day =nth day= .01*(2)^(n-1)
anonymous
  • anonymous
Plan A's function A(t) and PLan B's function B(t),
anonymous
  • anonymous
ok so my question is how would i figure out the salary using that equation for plan B
anonymous
  • anonymous
add up each day

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