College Algebra

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20. Growth of an Account If Russ (see Exercise 19) chooses the plan with continuous compounding, how long will it take for his $60,000 to grow to $80,000?
3. (1/8) to the 2x-3= 16 to the x +1
13. e to the 4x= 4 to the x-2
15. ln (x-4) ln 3= ln(1/5) to the x power
20. Tripling Time For any amount of money invested at 6.8% annual interest compounded continuously, how long will it take to triple?
Please someone help ASAP!!!!!!!!! I don't understand any of these college algebra problems.

  • College Algebra -

    19
    you want to solve for t
    60000 e^.0675t = 80000
    e^.0675t = 1.333...
    ln both sides and use rules of logs
    .0675t lne = ln 1.3333... ( but lne = 1)
    t = ln 1.3333../.0675 = 4.26 years, appr 4 years and 3 months

    3.
    (1/8)^(2x-3) = 16^(x+1)
    (2^-3)^(2x-3) = (2^4)^(x+1)
    2^(-6x + 9 = 2^(4x + 4)
    -6x + 9 = 4x + 4
    -10x = -5
    x = 1/2

    13.
    e^(4x) = 4^(x-2)
    ln both sides

    4x lne = (x-2)ln4
    4x = ln4 x - 2ln4
    4x - ln4 x = -2ln4
    x(4 - ln4) = -2ln4
    x = -2ln4/(4-ln4)
    = appr -1.0608

    15. ln(x-4) ln3 = ln(1/5)^x

    no simple algebraic way to solve this, unless I misread the question. I took it the way you typed it
    ran it through Wolfram and Wolfram ran out of time trying to solve it

    http://www.wolframalpha.com/input/?i=solve++ln%28x-4%29*ln3+%3D+ln%281%2F5%29%5Ex

    20. solve

    1 e^.068t = 3
    now do it the same way as #19

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