anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
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,\[x=10\ln (\frac{1}{R}-\frac{1}{100})\]
anonymous
  • anonymous
lol...wait, I've stuffed it.
anonymous
  • anonymous
are you sure thats right?

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anonymous
  • anonymous
No, I'm checking, but I'm juggling a few things atm
anonymous
  • anonymous
Can I ask, is your equation right?
anonymous
  • anonymous
lokisan can u help me
anonymous
  • anonymous
If you solve that thing for x, you get a complex logarithm.
anonymous
  • anonymous
I'll see if I can help, imrickjames.

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