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Math Help - Exponential and logarithmic function help!

  1. #1
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    Exponential and logarithmic function help!

    Genaro is offered a weekly salary of $2000. Instead, Genaro makes the following counteroffer, "Pay me just one penny the first week, two pennies the second week, four pennies the next week, and so on. Doubling my salary each week."

    Question 1 says to fill in a table of values for the different salary options.. and this is what I have:
    Code:
    Week #       Salary option 1      Total cumulative salary option 1   
    1                       2000                          2000                              
    2                       2000                          4000                             
    3                       2000                          6000                              
    4                       2000                          8000                              
    5                       2000                          10,000                           
    6                       2000                          12,000                           
    7                       2000                          14,000                          
    8                       2000                          16,000                           
    9                       2000                          18,000                          
    10                     2000                          20,000                          
    15                     2000                          30,000                          
    20                     2000                          40,000                         
    25                     2000                          50,000                           
    X                      2000                          (Unsure what goes here for X

    Code:
    Week    Salary 2            Cumulative salary for option 2
    1            .01                      .01     
    2            .02                      .03 
    3            .03
    4            .04
    5            .05
    6            .06
    7            .07
    8            .08
    9            .09
    10          .10
    15          .15
    20          .20
    25          .25
    X            ????
    Am I correct in adding .4 pennies to the .3 pennies, because he wants it to add more each week? .. Can someone help me figure out how many pennies goes in each slot by week? : <
    I'm not necessarily looking for straight up answers.. but an explanation on how to get them..

    ..Then I have to set up a function which gives the cumulative weekly salary for Week#X for both of the salary options.. I'm not sure how to go about trying to set up my functions..

    Option 1 _____________
    Option 2 _____________
    Last edited by Skyshadows; November 27th 2012 at 02:38 PM.
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  2. #2
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    Re: Exponential and logarithmic function help!

    You can use the [code]...[/code] tag to preserve alignment.

    Why does the table say that salary 2 for week #3 is .03? Shouldn't it be two times more than the previous week?

    Quote Originally Posted by Skyshadows View Post
    Then I have to set up a function which gives the cumulative weekly salary for Week#X for both of the salary options.. I'm not sure how to go about trying to set up my functions..
    With salary 1, Genaro receives $2000 every week. Are you sure you don't know how much in total he receives in x weeks? Multiplication is usually covered in elementary school...
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  3. #3
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    Re: Exponential and logarithmic function help!

    Emakarov-


    The salary option 2, is .03 in week 2, not 3. : < Sorry.. My mistake.


    Well, I understand the multiplication aspect, but.. The functions are where I am having an issue. It's just setting up what the function looks like, I can solve it from there..

    I'm sorry if this is confusing..
    I'm aware this is probably a super easy problem to solve, but.. I always get marked down for little mistakes and I'm looking to make sure I get it right this time.
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  4. #4
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    Re: Exponential and logarithmic function help!

    Quote Originally Posted by Skyshadows View Post
    The salary option 2, is .03 in week 2, not 3.
    Then I have to repeat what I said replacing "week #3" with "weak #2":
    Quote Originally Posted by emakarov View Post
    Why does the table say that salary 2 for week #2 is .03? Shouldn't it be two times more than the previous week?
    Quote Originally Posted by Skyshadows View Post
    Well, I understand the multiplication aspect, but..
    Then how much does the person earn in x weeks if he earns $2000 per week?

    Quote Originally Posted by Skyshadows View Post
    The functions are where I am having an issue.
    In this context, a function is just an arithmetic expression. After you figure out how much the person earns in x weeks under option 1, you'll get an expression that contains x. This expression determines a function: given any concrete x, the expression evaluates to a concrete number, the value of the function at x.
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  5. #5
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    Re: Exponential and logarithmic function help!

    I believe this is a geometric progression where the formula to find the total pennies for any given day is 2^n - 1 pennies, where n is the number of weeks. The equation for the first example is 2000x where x is the number of weeks.
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  6. #6
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    Re: Exponential and logarithmic function help!

    I figured that's what I was dealing with, I just have a hard time with trying to set up the equations.. Thanks Watt- I had 2(x-1) .. Which now I know makes no sense. Thank you for your help!
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