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Math Help - Eponential Functions

  1. #1
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    Eponential Functions

    Okay, I have tried for 2 hours on this, and I'm sure it is going to turn out to be one of those questions where it is a lot simpler than it seems but, here goes, I would love for anyone to help and explain how they did it too.

    7. Your mother is pleased you are going to make an effort to make your bed, so she agrees that each day you make your bed, she will nag you half as long about your other household chores. She currently nags you for 120 minutes a day.

    a) If n is the day number, and M is the number of minutes spent nagging, write a relation for n and M

    b) How much will your mother nag on the 28th day?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by penragonwebsite View Post
    Okay, I have tried for 2 hours on this, and I'm sure it is going to turn out to be one of those questions where it is a lot simpler than it seems but, here goes, I would love for anyone to help and explain how they did it too.

    7. Your mother is pleased you are going to make an effort to make your bed, so she agrees that each day you make your bed, she will nag you half as long about your other household chores. She currently nags you for 120 minutes a day.

    a) If n is the day number, and M is the number of minutes spent nagging, write a relation for n and M
    ok, let's take this in steps so that you see the process. let us assume that you make your bed everyday since she told you that.

    day 0 (before you start making your bed): M = 120

    day 1 (1 day after you start making your bed): M = 120 \cdot \frac 12 = 120 \left( \frac 12 \right)^1 .........half as much as the previous day

    day 2: M = 120 \cdot \frac 12 \cdot \frac 12 = 120 \left( \frac 12 \right)^2 ............half as much as previous day

    day 3: M = 120 \cdot \frac 12 \cdot \frac 12 \cdot \frac 12 = 120 \left( \frac 12 \right)^3 ..............half as much as previous day

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    .
    .
    see the pattern? the exponents of the 1/2 matches up with the number of days. the relationship is: M = 120 \left( \frac 12 \right)^n

    b) How much will your mother nag on the 28th day?
    you should be able to figure this out now
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  3. #3
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    thank you so much! I knew about the dividing it in half each time, but I was not able to put it into an equation.
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