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Math Help - rate question

  1. #1
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    Question rate question

    Question asks to find the rate of atmospheric pressure changing for a rocket rising vertically at 5km/s when at an altitude of 1km.
    Given the relationship of atmospheric pressure (in milibars) at an altitude of x kilometres is given by 1000(0.88)^x.

    I just can't see how to differentiate the function. Anyone?
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  2. #2
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    integrate?

    the question is asking for a rate of change ... sounds like a derivative to me.
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  3. #3
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    Question

    Sorry yes I meant differentiate, I cannot see how to differentiate it.
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  4. #4
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    \frac{d}{dt} a^x = a^x \cdot \ln{a} \cdot \frac{dx}{dt}
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    Question

    Is this right?
    <br />
\begin{array}{l}<br />
 \frac{d}{{dt}}P(x) = \frac{d}{{dt}}[1000(0.88)^x ] \\ <br />
  = 0.88^x \ln (0.88)\frac{{dx}}{{dt}} \\ <br />
 \end{array}<br />
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  6. #6
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    Question

    Is this right?
    <br />
\begin{array}{l}<br />
 \frac{d}{{dt}}P(x) = \frac{d}{{dt}}[1000(0.88)^x ] \\ <br />
  = 0.88^x \ln (0.88)\frac{{dx}}{{dt}} \\ <br />
 \end{array}<br />
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  7. #7
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    what happened to the constant 1000?
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