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Math Help - Please help with these function problems!

  1. #1
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    Please help with these function problems!

    Hey guys any help I could get on these few questions would be amazing. Thanks!

    1) Find the average rate of change of the function f(x)=e^x - e^(-x) as x goes from -3 to -1. Give an exact answer (in terms of e) and an approximate answer (rounded to the nearest thousandth.)

    2) If an investment of $2000 grows to $2700 in three and a half years, with an annual interest rate that is compounded quarterly, what is the annual interest rate?

    3) Sketch the graph of the function: g(x) = 2 ln x+3 (label 2 points with exact coordinates.)

    4) Students in a precalculus class were given a final exam. Each month thereafter, they took an equivalent exam. The class average on the exam taken after t months is given by F(t)=82-8(ln(t+1)). a) What was the class average after 6 months? b) After a year? c) When did the class average drop below 55? (Approx. answers with values rounded to nearest thousandth.)
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  2. #2
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    Quote Originally Posted by antz215 View Post
    Hey guys any help I could get on these few questions would be amazing. Thanks!

    1) Find the average rate of change of the function f(x)=e^x - e^(-x) as x goes from -3 to -1. Give an exact answer (in terms of e) and an approximate answer (rounded to the nearest thousandth.)
    The rate of change is,
    f'(x) the derivative.
    The avergae value is,
    \frac{1}{-1+3}\int_{-3}^{-1} f'(x)dx
    But by fundamental theorem the integral of derivative is the original function! Thus, I did not even have to integrate that expression it return back to itself.
    \frac{1}{2}\cdot (f(-1)-f(-3))
    Is the answer.
    Evaluate to get a numerical answer.
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