Question

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

Answer 1

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,\[x=10\ln (\frac{1}{R}-\frac{1}{100})\]

Answer 2

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

Answer 3

are you sure thats right?

Answer 4

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

Answer 5

Can I ask, is your equation right?

Answer 6

lokisan can u help me

Answer 7

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

Answer 8

I'll see if I can help, imrickjames.