## 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

1. 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,$x=10\ln (\frac{1}{R}-\frac{1}{100})$

2. anonymous

lol...wait, I've stuffed it.

3. anonymous

are you sure thats right?

4. anonymous

No, I'm checking, but I'm juggling a few things atm

5. anonymous

Can I ask, is your equation right?

6. anonymous

lokisan can u help me

7. anonymous

If you solve that thing for x, you get a complex logarithm.

8. anonymous

I'll see if I can help, imrickjames.