Our new Indie Games subforum is now open for business in G&T. Go and check it out, you might land a code for a free game. If you're developing an indie game and want to post about it, follow these directions. If you don't, he'll break your legs! Hahaha! Seriously though.
Our rules have been updated and given their own forum. Go and look at them! They are nice, and there may be new ones that you didn't know about! Hooray for rules! Hooray for The System! Hooray for Conforming!
Calculus Exam in 1 hour. New problem in OP
TL DROn this, reasonable people can disagreeRegistered Userregular
Hi, H/A. As usual, I will be taking full advantage of our resident math gurus in my time of need. Thanks in advance!
The population of Austria, P, in millions, is given by
P(t) = 5:6 (0.994)^t where t is time in years since 2000. How fast (in people/year) will it be changing in 2010?
I know that the answer is
P'(t) = 5.6 (0.994) ln (0.994)
= -31,733 people/year
I do not know where the ln (0.994) bit comes from. Is it some special property of the derivative of a number ^10? Something to do with the chain rule? Thanks again. I'll be adding problems as they come along.
The average cost per item to produce q items is given by a(q) = q^2 - 90q +3500. Find the minimum value of the marginal cost. (Hint: First find the total cost C(q), and then MC(q). Then minimize MC(q).)
So to get C(q) I would just multiply the a(q) function by q, since (average cost per unit) times (number of units) = (total cost), right?
That gives me C(q) = q^3 - 90q + 3500q.
Marginal cost would be the derivative, correct? C'(q) = 3q^2 - 180q + 3500
I believe the next step is to set the function equal to zero to get the critical point(s). 0 = 3q^2 - 180q + 3500 3500 = 3q^2 - 180q
And here I am stuck. Thanks again for the assistance.