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Math Help - Exp Function Word Problem

  1. #1
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    Exp Function Word Problem

    One day, a controversial video is posted on the Internet that seemingly gives concrete evidence of life on other planets. Suppose that 50 people see the video the first day after it is posted and that this number doubles everyday after that.

    a) write an expression to describe the number of people who have seen the video t days after it is posted.

    b) one week later, a second video is posted that reveals the first as a hoax. Suppose that 20 people see this video the first day after it is posed and that this number triples every day after that. Write an expression to describe the number of people who have seen the 2nd video t days after it is posted.

    c) set the two expressions from parts a and b to equal each other and then solve for t. What does this solution mean?

    Ok can you just check my answers for parts a and b, except for part c i dont know what this means.

    a) A(t)=50(2)^t
    b) A(t)=20(3)^t
    c) I set them equal to each other and the variable disappeared on me..ie cancelled out What does this mean?
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  2. #2
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    Quote Originally Posted by skeske1234 View Post
    One day, a controversial video is posted on the Internet that seemingly gives concrete evidence of life on other planets. Suppose that 50 people see the video the first day after it is posted and that this number doubles everyday after that.

    a) write an expression to describe the number of people who have seen the video t days after it is posted.

    b) one week later, a second video is posted that reveals the first as a hoax. Suppose that 20 people see this video the first day after it is posed and that this number triples every day after that. Write an expression to describe the number of people who have seen the 2nd video t days after it is posted.

    c) set the two expressions from parts a and b to equal each other and then solve for t. What does this solution mean?

    Ok can you just check my answers for parts a and b, except for part c i dont know what this means.

    a) A(t)=50(2)^t
    b) A(t)=20(3)^t
    c) I set them equal to each other and the variable disappeared on me..ie cancelled out What does this mean?
    I've noticed you've posted quite a few questions on exponential functions - if you're struggling it would be better to ask your tutor if you don't understand.

    A and B are fine. C will require logs to find t

    50 \times 2^t = 20 \times 3^t

    Divide through by 20:

    2.5 \times 2^t = 3^t

    Take logs:

    ln(2.5 \times 2^t) = ln(3^t) = t \times ln(3)

    Use the law ln(a) + ln(b) = ln(ab)

    ln(2.5) + t \times ln(2) = t \times ln(3)

    Can you solve it from here?

    Spoiler:
    Get t onto one side and factorise

    t(ln(2) - ln(3)) = -ln(2.5)

    Divide through by ln(2)-ln(3)

    t = -\frac{ln(2.5)}{ln(2)-ln(3)} = \frac{ln(2.5)}{ln(3)-ln(2)}

    That will be some irrational number and it will give the number of days for them to be equal
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