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Math Help - Exponential Functios questions help?

  1. #1
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    Exponential Functios questions help?

    1.
    3^(x-2)=5^x
    2^(x-2)=3^(x+1)

    cant use log.

    2. Lucas is hoping to take a vacation after he finishes university. To do this he needs $5000, he finishes with $3500 in an investment that pays 8.4 per year, compounded quarterly. how long will Lucas have to wait before he has enough money to go on vacation.

    I did 3500*1.084^x/4 wrong results
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    Re: Exponential Functios questions help?

    You can't solve either of question 1 without logarithms.
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    Re: Exponential Functios questions help?

    Hello, skg94!

    1(a)\;3^{x-2}\:=\:5^x
    . (b)\;2^{x-2}\:=\:3^{x+1}

    Can't use log. . Then they can't be solved.


    2. Lucas is hoping to take a vacation after he finishes university. .To do this he needs $5000.
    He has $3500 in an investment that pays 8.4% per year, compounded quarterly.
    How long will Lucas have to wait before he has enough money to go on vacation?

    The formula is: . A \;=\;P(1 + i)^n

    . . where: . \begin{Bmatrix} P &=& \text{principal invested} \\ i &=& \text{periodic interest rate} \\ n &=& \text{number of periods} \end{Bmatrix}

    We have: . P = 3500,\;i = \frac{0.084}{4} = 0.021,\;n = 4x
    . . where x is the number of years.

    Then: . 3500(1.021)^{4x} \:=\:5000 \quad\Rightarrow\quad (1.021)^{4x} \:=\:\tfrac{10}{7}

    Take logs: . \ln(1.021)^{4x} \:=\:\ln\left(\tfrac{10}{7}\right) \quad\Rightarrow\quad 4x\ln(1.021) \:=\:\ln\left(\tfrac{10}{7}\right)

    Therefore: . x \;=\;\frac{\ln(\frac{10}{7})}{4\ln(1.021)} \;\approx\;4.29\text{ years}
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    Re: Exponential Functios questions help?

    my answer says its 4.5

    its nice to know the interest formula though, if i were to graph it which formula would i use?

    3500(1+(.084/4)^4x ?
    or 3500 * (1.021)^4x

    well the thing is while i know how to do log, my test tomorrow will strictly be using expontential fuctions only, so i guess my teacher made a mistake in this review
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    Re: Exponential Functios questions help?

    Why would you think that a test on exponential functions wouldn't include logarithms? Logarithms are the inverse functions of exponentials, and so MUST be used in many cases involving exponential functions, such as the ones above.
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    Re: Exponential Functios questions help?

    Because the the teacher hasnt taught it so i cant be tested on something i havent been taught?
    If he gives a test on lessons he hasnt even mentioned then how can i be expected to answer them.
    I know log because i was told to do this using log, but seeing as how i wouldnt be able to use them on a quiz where i havent learned logs i decided to ask if there is a way without them, which there isnt
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