Urgent!Calculus problem *4?

1.The Math editor at a major publishing house estmates that if x thousand complimentary copies are distributed, the 1st yr sales of a certain new mathematics text will be aprroximately f(x)=20-15e^-.2x thousand copies.


a.how many copies can be expect to sell in the 1st-yr if no comlimentary copies are sent out?


b.how many copies can be expect to sell in the 1st-yr if 10,000complimentary copies are sent out?


c.If the estimate is correct,what is the most optimistic projection for the 1st-yr sales of the text?





2.A business estimates that when x thousand ppl are employed,its profit will be p(x)million dollars, where P(x)=10+In(x/25)-12x^2 for x%26gt;0.What level of employment max. and min. profits?





3.V(t)=Vο(1-2/L)^t where V(t)is the value after t yrs of an article that originally cost Vο dollars%26amp;L is a constant


a.refrugerator cost$875 %26amp; has useful life of 8yrs.what is tis value after 5yr?what is its annual rate of depreciation?


b.what is the %rate of change of V(t)?

Urgent!Calculus problem *4?
1a and 1b just involve plugging numbers in to the definition of f.





For 1c, it turns out that f' is never 0. So the maximum will be at an endpoint of the possible interval.





(Unless you made a typo, which seems likely, as the phrasing is a bit weird.)





For 2, try setting P' = 0. That turns out to be, in effect, a quadratic equation in x, so solving it isn't hard. Presumably, one root gives the minimum and one gives the maximum.





3 is a combination of finding dV/dt and plugging values in. Recall that C^t = e ^ (t lnC), which makes it easy to differentiate C^t when C is a constant.