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    Polynomial functions, inverses, half-life, investments

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    1) Fit a polynomial Function f(x) to the graph. The scale on the x-axis is 1 and the scale on the y-axis is 5. The point (1,12) is on the graph, Assume that if the graph appears to cross the x-axis at a mark, it really does.

    (1,12)
    3
    2
    1 4

    2) Noise level in decibels as it depends on the sound intensity (I, in watts/cm2) is defined by the following formula, when Io is the faintest sound the human ear can hear.

    DB=10 log (I/Io). where Io= 1x10-16watts/cm2

    A) What is the noise level for a sound with intensity 2.5 x 10-9watts/cm2

    B) A typical noise level at a rock concert is about 110dB. What is the sound intensity for this noise level?

    C) How many times more intense is a 110dB noise than a 45 dB noise?

    3) Find the inverse of f(t) = 3t-7/5. if it exists. Check using function composition.

    4) Find the time it will take a sample of Plutonium-239 to decay to 0.50% of its original amount if Plutonium-239 has half-life of 24,100 years.

    5) How long would it take to triple an investment of $30,000 if it is compounded quarterly at 5.25% annual interest rate?

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    https://brainmass.com/math/graphs-and-functions/polynomial-functions-inverses-half-life-investments-35774

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    Please see the attachment.

    1) Fit a polynomial Function f(x) to the graph. The scale on the x-axis is 1 and the scale on the y-axis is 5. The point (1,12) is on the graph, Assume that if the graph appears to cross the x-axis at a mark, it really does.

    (1,12)
    3
    2
    1 4

    Answer: the Polynomial is y = 3.625x3 - 21.375x2 + 26.75x + 3

    2) Noise level in decibels as it depends on the sound intensity (I, in watts/cm2) is defined by the following formula, when Io is the faintest sound the human ear can hear.

    DB=10 log ...

    Solution Summary

    This solution is comprised of a detailed explanation to solve olynomial functions, inverses, half-life, and investments questions.

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