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anonymous

  • 5 years ago

If R is the percent of maximum response and x is the dose in mg, the dose-response curve for a drug is given by R=100/1+100e^-0.1x What dose to the nearest integer corresponds to a response of 50% of the maximum

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  1. anonymous
    • 5 years ago
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    R is the percent of maximum response, and you're asked to find the dose (to nearest integer) where that percent is 50%. Since you're asked to find x, it's best to solve for it first, then put your numbers in. So\[R=\frac{100}{1+100e^{0.1x}} \rightarrow R(1+100e^{0.1x})=100\]i.e.\[100e^{0.1x}=\frac{100}{R}-1 \rightarrow e^{0.1x}=\frac{1}{R}-\frac{1}{100}\]Now take the natural logarithm of both sides, so that\[\ln e^{0.1x}=\ln (\frac{1}{R}-\frac{1}{100}) \rightarrow 0.1x=\ln (\frac{1}{R}-\frac{1}{100})\]and dividing by 0.1,\[x=10\ln (\frac{1}{R}-\frac{1}{100})\]

  2. anonymous
    • 5 years ago
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    lol...wait, I've stuffed it.

  3. anonymous
    • 5 years ago
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    are you sure thats right?

  4. anonymous
    • 5 years ago
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    No, I'm checking, but I'm juggling a few things atm

  5. anonymous
    • 5 years ago
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    Can I ask, is your equation right?

  6. anonymous
    • 5 years ago
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    lokisan can u help me

  7. anonymous
    • 5 years ago
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    If you solve that thing for x, you get a complex logarithm.

  8. anonymous
    • 5 years ago
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    I'll see if I can help, imrickjames.

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