Applications of the Derivative

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Ulva

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hey I'm studying for my calculus exam tomorrow and going over the review I am having a lot of trouble with some word problems dealing with revenue and profit margin and whatnot. Hope you guys can help, here's the problem.

At the moment, OHaganBooks.com is selling 1000 books per week and its sales are rising at a rate of 200 books per week. Also, it is now selling all its books for $20 each, but its price is dropping at a rate of $1 per week. At what rate is OHaganBooks.com's revenue rising or falling?

I'm not even really sure how to begin :(
 
Ulva said:
hey I'm studying for my calculus exam tomorrow and going over the review I am having a lot of trouble with some word problems dealing with revenue and profit margin and whatnot. Hope you guys can help, here's the problem.

At the moment, OHaganBooks.com is selling 1000 books per week and its sales are rising at a rate of 200 books per week. Also, it is now selling all its books for $20 each, but its price is dropping at a rate of $1 per week. At what rate is OHaganBooks.com's revenue rising or falling?

I'm not even really sure how to begin :(
Click to expand...

Let

cost of each book = C

no.of books sold per week = N

then

Weekly revenue = R = C * N

Your problem asks you to find dR/dt.

Continue...
 
when you say R = C * N do you mean C multiplied by N or C to the power of N?
 
so we end up with R(x) = (1000)(20) which is 20,000x
And if we're looking for dR/dt then we must take the derivative of R which would be 20,000 and place it over the derivative of t.
For every one week the sales increase by 200 books and the price drops by $1
This is where things really get tricky for me, how would I make a function out of this? does it have to do with Pe^rt?
 
Ulva said:
so we end up with R(x) = (1000)(20) which is 20,000x .... No you don't end-up with that ... where did 'x' come from?
And if we're looking for dR/dt then we must take the derivative of R which would be 20,000 and place it over the derivative of t.
For every one week the sales increase by 200 books and the price drops by $1
This is where things really get tricky for me, how would I make a function out of this? does it have to do with Pe^rt?
Click to expand...
 
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