#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;

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!