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Thread: please help with algebra: exponential functions

  1. #1
    Mar 2008

    Post please help with algebra: exponential functions

    hi, i've been working on my homework that's due tomorrow, and i'm nearly done, but these are the only problems i've had trouble with. all questions are non-calculator, so steps would be appreciated:

    The graph of the function f(x)= 3e^x-4 has an asymptote of

    a) x= -4
    b) x= 3
    c) y= -4
    d) y= 3
    e) y=x

    What are the steps for solving this? i haven't been given a formula. isn't the first step to find ln of the equation? how do i go about doing that?

    Radioactive substance decreases by 10% per hour. if there were 64 grams of the substance at time t=1, which of the following exponential functions models the amount, R, in grams of the substance as a function of the time, t, in hours?

    a) R= 54(1.10)^t
    b) R= 60(1.10)^t
    c) R= 48.6(1.10)^t
    d) R= 54(.90)^t
    e) R= 60(.90)^t

    The equation for the decay function is A(t)= a(1-r)^t, I believe. I came up with 1= 54(.90)^t as my answer, so that's d, but i am not completely sure..

    k(x)= 4^x, then k(x-2)=

    a) 1/16(4^x)
    b) 1/2(4^x)
    c) 4^x-16
    d) 4^x-2
    e) (1/16)^x

    I know that since it is not asking for k(x)-2, d is definitely not a correct answer. k(x-2)= 4^(x-2), so what are the next steps??

    I have this table of values:
    x | -1 | 0
    f(x)|-6 | -2
    I need to make it into an exponential function. What are the steps I should take?
    Choices are:
    a) y= 2(-3)^x
    b) y= -2(-3)^x
    c) y= -2(3)^-x
    d) y= 1(-6)^x
    e) y= -1(6)^x

    Population of students at school is modeled by function P(t)= 500(1.12)^t, where t is the number of years since 1995. With this model, by what % is the popilation of the school changing each year?

    a) 400%
    b) 112%
    c) 88%
    d) 12%
    e) 4%

    i'm guessing d, 12%, since this seems to be following the growth formula A(t)= a(1+r)^t, am I right?

    i hope you can help, thank you!!!
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  2. #2
    Feb 2008
    Westwood, Los Angeles, CA
    I'll tackle a couple.

    #1) Are there any values of x you CAN'T put into your function $\displaystyle f(x) = 3e^x -4$? Doesn't look like it - pretty much anything will work for x.

    Are there any values you CAN'T get out for f(x)? Look at that e^x. Can it ever equal zero? Nope - an exponential function can never equal zero. That means 3e^x can't be zero, so 3^x - 4 can never be -4. Based on that, I choose c.

    #3) You're right - you have $\displaystyle 4^{(x-2)}$. That's the same as:

    $\displaystyle \frac{4^x}{4^2}$ (remember when you divide powers with the same base, you can subtract the exponents; thus, you can rewrite a difference of exponents as division - that sounds a little confusing, but hopefully makes sense).

    I'll leave it to you to simplify the above.

    #4) Since it's multiple choice, I would just try plugging in both x-values into each of your 5 choices and seeing which function works (i.e., gives you the correct f(x) values) for the information you're given.
    Last edited by Mathnasium; Mar 26th 2008 at 07:46 AM.
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