# Word problems, half life ...

• Jan 14th 2009, 07:36 PM
lic2kill
Word problems, half life ...
#1
Drug X is administered in a single 500 mg dose and has a half-life in the bloodstream of 32 hrs. Drug Y is administered in a single 700 mg dose and has a half-life in the bloodstream of 25 hrs. How many hours will it take for the concentration of drug X to drop below the concentration of drug Y?

#2
If an object emitting light at a frequency f is moving toward an observer at a velocity v, then the light's frequency f' as seen by the observer is related to the frequency emitted by the object by the relativistic Doppler shift formula;
http://www.texify.com/img/%5CLARGE%5...c%7D%7D%7D.gif
where c is the speed of light. Find the velocity in terms of the speed of light, at which the observed frequency is twice the emitted frequency.

#3
The cost C for a manufacturer to produce u units of a new light bulb is given by the function c(u)= 75,000 + .45u. The manufacterer conducts market research which shows that the number of units sold S is related to the price p by the function S(p)+ 250,000 - 86000p.

a. Find a formula for the composite of C with S:
Which is 75,000 + .45(250,000 - 86000p)

b. What does the function the composite C with S represent?
The cost due to the amount sold?

c. find a formula for the revenue R as a function of the price p.
250,000 - 86000pē
d. Find a formula for the function
F= R - composite of C with S.
*edit* -86000pē-38700p+287500=0 ?
e. What does the function F represent?
*edit* Total profit ?
Thanks for the help!
• Jan 15th 2009, 03:36 AM
stapel
Quote:

Originally Posted by lic2kill
#1 Drug X is administered in a single 500 mg dose and has a half-life in the bloodstream of 32 hrs. Drug Y is administered in a single 700 mg dose and has a half-life in the bloodstream of 25 hrs. How many hours will it take for the concentration of drug X to drop below the concentration of drug Y?

Create the exponential-decay formulas for the two concentrations. Note which drug is initially higher in concentration. Set the two formulas equal and solve for the time when the concentrations are equal, after which point the other drug will then be higher in concentration.

Quote:

Originally Posted by lic2kill
#2 If an object emitting light at a frequency f is moving toward an observer at a velocity v, then the light's frequency f' as seen by the observer is related to the frequency emitted by the object by the relativistic Doppler shift formula;

where c is the speed of light. Find the velocity in terms of the speed of light, at which the observed frequency is twice the emitted frequency.

I think this is just asking you to solve the equation for "v=".

Quote:

Originally Posted by lic2kill
#3 The cost C for a manufacturer to produce u units of a new light bulb is given by the function c(u)= 75,000 + .45u. The manufacterer conducts market research which shows that the number of units sold S is related to the price p by the function S(p)+ 250,000 - 86000p.

a. Find a formula for the composite of C with S:
Which is 75,000 + .45(250,000 - 86000p)

Yes, but you may be expected to simplify this.

Quote:

Originally Posted by lic2kill
b. What does the function the composite C with S represent?

The cost due to the amount sold?

The proper lingo might be "the cost of producing the units which have been sold."

Quote:

Originally Posted by lic2kill
c. find a formula for the revenue R as a function of the price p.250,000 - 86000pē

Looks good.

Quote:

Originally Posted by lic2kill
d. Find a formula for the function F= R - composite of C with S.
*edit* -86000pē-38700p+287500=0 ?

I haven't checked the math, but if you subtracted (a) from (c) correctly, you should be fine.

Quote:

Originally Posted by lic2kill
e. What does the function F represent? *edit* Total profit ?

The difference between income (direct revenues) and outgo (raw production costs) is, yes, usually called "profit" or "gross profit". :D