# A few questions I'm really stuck on

#### luejinX

##### New member
Hi,

I have a bunch of problems to do and I've figured out all of them except for these two. If anyone could help me understand how to properly figure out these two problems, I would appreciate it very much!

1)
The poll results are given as 47% support for candidate 'A' with an error margin of plus or minus 3% with a confidence interval of 19/20. What margin of error should be given for a confidence of:

a) 99.7%
b) 68%
I know the margin of error is (47% + 3% = 50%) (47% - 3% = 44%). I'm not really sure how to figure out the confidence intervals for a) and b)

I'm really stuck here so any help in the right direction would be very helpful.

2)
A drug is given to a person by injecting 20mg of the substance. The drug is processed and removed from the body in such a way that the amount remaining is halved every two hours. How long does it take for there to be 6mg of the drug remaining in the person's body?
I was told this has to do with log base 2 and exponential decay (y=s x 2^-t) but again, I'm stuck and not exactly sure how to follow the appropriate steps in solving this.

Any hints, tips or walkthroughs on these problems would be much appreciated.

Thank you!

#### galactus

##### Super Moderator
Staff member
The second one can be found very easily by using the fact that half-life is $$\displaystyle T=\frac{-1}{k}ln(2)$$

$$\displaystyle 2=\frac{-1}{k}ln(2)\Rightarrow k=\frac{-ln(2)}{2}$$

Now, using $$\displaystyle y=y_{0}e^{kt}$$ we can find the time, t, until only 6 mg are left.

$$\displaystyle 6=20e^{\frac{-ln(2)}{2}t}$$

Solve for t.

#### luejinX

##### New member
I appreciate the fast response, but you may need to dumb it down a little bit for me. :?

#### luejinX

##### New member
Is it 3 hours, 28 minutes?